When I bought my used bike, it had an 80 mm stem on it. It was too short, so I tried a 100, then a 90. If it is indeed true "the longer the stem, the better control", that was totally lost on me. There was no difference in "handling", but definite difference in position comfort. I ended up with a 90. I'm now in the process of experimenting with shallower drop bars, which happen to have shorter reach. I'm going to ride them for a while with the 90, and then decide if I want to try the 100 again.
I really doubt that you'll notice a difference in handling if you either go down to an 80mm stem with your current bars, or keep the 90 and get a shorter reach bar. Frankly, I doubt anyone would notice that difference; I don't believe it exists.
I don't think the price for experimenting would be much different either way, whether you try a new stem or new bars. In very general terms, from what I've seen, bars and stems of the same "category" (meaning relative weight) will cost about the same. " Light weight" alloy bars and stems retail for $75-100. Slightly heavier weight for either: $50-75 retail. Cheapest versions of either (again, slightly heavier): $30-$50. Forget carbon, but if you go that route, you'll see a similar price point.