Switching Twitter to timeline mode rather than their poor excuse of an algorithm helps. Learned that from HN....but I have a browser plug-in that also removes all their recommended and "Joe also owed this tweet" junk.
Funny enough I have the opposite opinion regarding twitter:
If I use it in timeline mode I have the urge to read through all of it until where I stopped last time as the OP described (same with my Feedly RSS feed)
In algorithm mode its more like a "don't care, its garbled anyway, just a sea of stuff".
That being said I am still mostly using timeline mode.