I did the power valve opening trick as noted in the article.
That did the trick on the little 1-1/16 carb.
But mainly, I like it cuz you are at most ruining the "tower" that holds the spring, jet, etc. You can swap in another one if you ruin it.

I have not tried drilling the idle passage in the air horn though it seems a reasonable fix to the hesitation. This is sometimes done when running a big cam when you need a lot more idle and transition volume of fuel/air. Bad part of this trick is, once you drill it you kinda ruin the lid if its too far, so then you have to swap on another similar carb lid.

Sounds like you fixed your problem though?
Yup those old tanks and the sender/filter/sock can get full of crud and goo.