Personally, after I moved Retweets to their own tab, I found I just never missed them or looked at them again, and if I put them back in it just seems like random noise now.
> And at the start of the session, move me to the last tweet I viewed
This one I would like to do, but... Twitter has at least some built-in ability to do this (if you scroll your timeline a few screens worth, navigate away from the home timeline then eventually navigate back, it can restore your previous position), but I haven't found a way to make use of it for this feature - I _suspect_ they're caching the current state of whatever way they do their windowing of timeline tweets, then restoring that later, which means it's probably not possible to leverage it to jump to a particular tweet from a cold start.
Automatically scrolling through tweets until you hit a particular last-seen one isn't great alternative either, as it's pretty slow and the timeline currently seems to end after about a day and a half.