"We tried 165, 170, 175 and 180 jets -- a pretty wide range -- and while we saw the effects, they didn't make a huge difference"

That changing the main jet doesn't alter midrange acceleration much is no surprise to me. One of the functions of emulsion tubes is that their diameter combined with the fuel level forms a reserve of fuel that has already gone past the main jet. It's this reserve of fuel that controls richness during the early part of acceleration & the main jet has no effect until the reserve has been spent.

To determine the main jet size, load it up on the dyno & hold it at say 4000rpm & pick the jet that gives the correct mixture, repreat this process at 6000 for the air correcton size. Hold it at 4700rpm & adjust the timing. You now have the correct main jet, air corrector & ignition timing for the worst conditions.
Any richness, leaness, backfiring, etc is the result of the wrong choice elsewhere.

Andrew's emulsion tube selection guide makes no sense at all, selection of emulsion tubes is based on the level of modifications to an engine not it's capacity. As you would know the main jet & air corrector determine the mixture during full load/no acceleration. The emulsion tube determines richness during acceleration. If you are overly rich at low to midling speed, changing the main jet is not what you would do, you should first change to a tube that has no low holes. If you still have excess richness you should then go to thicker tubes. If F16's are giving you grief by being too lean higher up, you should probably reduce the size of chokes. 38mm would be better for your requirements & still outflow anything that a 45mm DCOE can do.