Sorry, I didn't mean to convey that impression. Florida has been regularly reporting daily death counts that include deaths from several months ago.

I would need to know that the older, higher numbers were not also subject to the same delays.

They were, in the other direction. If you look at the date-of-death chart in the thread I linked, you'll see that for a few weeks there were consistently over 200 actual deaths per day, while the reported 7-day average in your chart never reached 200. The delay means that the reported count will be lower than the actual count when deaths are rising, and higher than the actual count when deaths are falling.

And of course we can't be sure which of those categories we're in at any particular point in time; if deaths do start to increase again, it may not be noticeable in the reported numbers for several days. But based on the hospitalization trend I believe it's probable that the current reported numbers overstate the actual deaths.