Solving gear hunting? Interesting problem on the only triple chainring bike I've ever owned (I've never run into this problem on a double chainring ever).  It has a 9-speed cassette.  In the middle chainring, the middle 3 rear gears hunt around.  Example, when in 5th sometimes it'll randomly jump up or down a gear.  6th, sometimes it'll jump down 1.  4th, sometimes it'll jump up 1.  It'll stay in the gear you put it for the majority of riding, but occasionally it'll suddenly just hunt around a little within that specific subset of gears and then settle down again.

It's been like that since brand new (2006, Cannondale with Shimano components, most notably the Flightdeck shifters).  My wife just lived with it (it was her bike originally).  When she crashed it (and gave up cycling), I inherited it and I also just lived with it for awhile.  Finally the last couple of years I've re-calibrated the shifting a few times in an attempt to solve this issue.  I can get everything spot on except for that pesky hunting right in the middle gears!

Tips/tricks specifically for adjusting shifting on these triple chainring bikes?
You don't mention checking the derailer hanger alignment is correct, which indicates a very high probability that's at least a partial contributor to the problem. Some Cannondale factory road hangers are among the most Play-doh-like ones around, although it's a common problem on most replaceable hanger road bikes. Aligning the hanger is a very routine step in getting the shifting correct. Doing it right does require a special tool, although roughing in a visually bent replaceable hanger in a pinch can be done by sticking a wrench in the mounting bolt, albeit at the cost of using up more of its fatigue life than doing a minimal number of bends with an alignment gauge would. Note there's always some risk of breaking a hanger while trying to align it, but most typical replaceable ones are made of very ductile material and it doesn't actually happen very often.

Cable tension misadjustment, cable friction, derailer wear, cassette wear are the other common factors here. If it's really and truly only ever skipping around in those 3 gears, you might look closer at the wear.

It's true that what front gear you're in can have an influence on how and whether the rear end misbehaves, but there's not really anything one does differently to adjust rear shifting on a triple versus a double or one-by, other than that you have one more chainring's worth of combinations to check through when test riding. If all the parameters that determine rear end performance are correct, there shouldn't be any issues. The exception is ultra-short chainstay bikes, like various terrible 650C tri/TT bikes, where the rear end can act like it's in a cross gear even when it's not, but not many bikes like that have triples and even if one did it wouldn't be acting up only in the middle ring, so it's probably not what's going on here.