Ultimately there’s not enough evidence to say with certainty either way. Insisting on one particular option, especially the less likely one, is suspicious.
I’m Romanian fwiw.
There is no evidence about such a "spreading", and especially no linguistic evidence.
We know that Proto-Albanian and Proto-Romanian have been in contact, but that gives no information about the extent of the area inhabited by speakers of Proto-Romanian in the opposite direction. The contact has existed regardless whether the area inhabited by speakers of Proto-Romanian has extended to the North of the Danube or not.
Likewise, even if we knew for sure that no Dacian word has been preserved in Romanian, that would give absolutely no information either pro or contra the immigration theory, because that has nothing to do with the Dacians, but it is about whether the Roman citizens of Dacia have continued to inhabit Dacia permanently, or not.
Therefore all known linguistic data fails to provide any kind of evidence either in favor or against the immigration theory, so such a theory should not be mentioned in a linguistic discussion, unless some new evidence is discovered.
While there exists no direct evidence either in favor or against the immigration theory, this theory is pretty much unbelievable, because it requires for Dacia to have been depopulated.
For the lowlands at the North of Danube it is plausible that they might have been seriously depopulated, especially during several centuries when many invasions have passed through them.
On the other hand, it is completely implausible that the highlands of the Carpathian mountains have ever been depopulated. Those mountains offered exceptionally good life conditions, especially for people whose main activity was raising sheep. With the exception of a very well organized state, like the Roman Empire, no distant authority could have extended its influence into the mountains, so after the Roman Empire abandoned Dacia and there no longer was any central administration, the locals were left to themselves but they had no incentive whatsoever to abandon their good lands.
There is absolutely no chance that any invasion force passing through the lowlands would have risked to lose time and supplies and people by going up into the mountains in attempts to chase some locals who did not have anything valuable enough to be worth the effort.
So for me at least, such a theory based on the premise that some beautiful mountains with everything needed by humans for a decent life and well protected against outside intruders could at any time in history remain empty, waiting for the next passer-by to settle there, is absolutely ridiculous.
As said before, this has nothing to do with linguistics, so it should not be mentioned there without a good reason.
The scenario that Romanian arrived from across the Danube does not require that the Romanian Carpathians were completely depopulated. Rather, it is possible that the region’s inhabitants first switched to Slavic – this is supported by a great deal of toponymic evidence – and then later both language shift and the arrival of other populations resulted in the extinction of the Transylvanian and Oltenian dialects of Common Slavonic in favor of Romanian and Hungarian instead.
Then, the contemporary view of the relationship between Romanian and Aromanian is not that they were mere sister dialects of Latin but split up at a much later date – they are too similar for an early split, and it appears that their first layer of Slavic loans is identical, so that means a split after the 6th century CE. The scenario that Romanian nationalists support requires believing that Aromanian results from Romanian speakers from Dacia migrating well to the southwest. That both Romanian and Aromanian came from the Central Balkans instead is viewed as vastly more likely, especially in the light of the advances in the reconstruction of early Albanian (because an array of evidence puts early Albanian in the Central Balkans, not Dacia).
> so after the Roman Empire abandoned Dacia and there no longer was any central administration, the locals were left to themselves
While I know that the story of their ancestors “left to themselves” after Rome withdrew from Dacia persists in Romanian pop culture, it never fit well with the facts. Romanian words like biserica ‘church’ suggest that Romanian’s Latin ancestor remained in contact with the rest of the Mediterranean world for a long time, because only after Constantine in the 4th century were basilica buildings used as Christian churches. Again, this would be easily explainable by an origin in the Central Balkans where those cultural contacts persisted.
There is no doubt that when the Slavs have passed through the former Dacia province a part of them have stopped and settled there while the others have continued their journey to the South of the Danube. This explains the Slavic toponyms and the many Slavic loanwords into Romanian.
In your variant, the newly settled Slavs have been much more numerous than the Proto-Romanians, so they eventually assimilated the latter.
But then, several centuries later, there was a miraculous population explosion of the speakers of Proto-Romanian at the South of the Danube (even if in reality it is much more likely that their number was dwindling, by being assimilated by the Slavs that were more numerous in the South) and this great number of Proto-Romanians created out of nothing gathered their belongings and moved at the North of the Danube, where they created new settlements among the Slavs, and this time, unlike a few centuries ago, the number of Proto-Romanians was much greater than that of the Slavs, so the assimilation proceeded in reverse direction, restoring a Romance language as the main language of the land.
While this variant does not need the unbelievable depopulation hypothesis, it requires an unbelievable hypothesis about huge oscillations it the number of Proto-Romanians, for which there exists no explanation and no evidence.
I hardly believe that anyone can say with a straight face that this hypothesis is more plausible than the hypothesis conforming to Occam's razor, i.e. that the Slavs have settled both at the North and at the South of the Danube, but more of them have settled at the South, which was the endpoint of their journey (stopped by the Eastern Roman Empire), while the fewer that have settled at the North were early quitters, who did not want to wait in the hope of finding better lands.
In both places the Slavs have found Proto-Romanians, but eventually in the South most Proto-Romanians have been assimilated by the Slavs, while in the North the reverse happened.
This hypothesis does not include any implausible element, while the other 2 variants need either a depopulation or huge unmotivated demographic oscillations, which both are phenomena never observed in history anywhere else and for each of them there is no evidence.
Words like "basilica" have been obviously brought by missionaries coming from the Eastern Roman Empire, who spread the Christian Faith, and they do not provide any information about the location where this happened.
In general, I don’t see the point to debate further, because debate is not something that occurs on general-public internet fora like this. It is something that occurs in the appropriate scholarly venues. My original post up above aimed to emphasize that the contemporary consensus within linguistics – though it is only very slowly trickling into popular-science publications – does not see a role for “Dacian” in the Albanian–Romanian lexical isoglosses, and that has some important consequences for the reconstruction of Balkan linguistic history. That emerging consensus exists regardless of what you or I write here.
And since you are a representative of one of the peoples involved in a political squabble, it might be best for you to sit this out: in general in linguistics, it is often people from outside a region that do the best work on that region’s linguistic history, since they have no dog in the regional ethnic battles.
[1] https://www.cetateadescaun.ro/produs/slavii-in-perioada-migr...
