I wonder if the problem was initially mid-described. Perhaps it's not
"slipping" at all, perhaps it's what many of us have long called "ghost
shifting."
Zack is friction-shifting Hyperglide 9. Hyperglide is designed to let
the chain sit on 2 adjacent sprockets at the same time without
clattering. Indexing can be tuned to make the shift perfectly; with
friction shifting you are dependent on auditory feedback to align the
chain, and it's largely absent.
So what does this mean in practice? My experience friction shifting
Hyperglide 8 was that I'd downshift approaching a light or stop sign,
and thought I was correctly aligned. I'd stop, and when loading up the
drive train on start-up, the bike would upshift with a BANG.
I switched that bike to index shift levers and all is well. I moved the
friction shifters to a bike running Hyperglide 7 and all is well there.
7 is spaced wider, i.e., the sprockets are farther apart from each
other, making it easier to align the chain.
I also discovered something entirely counter-intuitive and counter to
long established "old timey" practice. In the old days, when you
downshifted you relieved pedal pressure on the drive train. That made
shifting much easier. What I found with Hyperglide is that if you load
the drive train, i.e., put pressure on the pedals, the downshift becomes
snappier and more positive, engaging the next sprocket with a clunk.