I'm gonna try not to write a book here.....
Crackedback has a pretty tried & true method for determining what initial timing a engine likes and will tolerate. Short version and not to put words in his mouth, it involves bringing the engine to operating temperature and bumping the initial around two degrees at a time until you sense a hesitation or kickback on the starter. When that occurs, you back the initial off a few degrees and drive it normally and also with a "moderate" amount of throttle up thru the mechanical curve, somewhere up to about 3500/4000rpm's. DO NOT HAMMER ON IT. If there's no "ping" issues, you found what it likes and then you restrict the total timing back to the 34/36* range. It's time consuming, but it works.
The reason that initial timing is so important is, it determines the vacuum signal to the carb, which determines the (idle speed) throttle blade position on the idle transfer slot, which is where all the idle, low speed settings/adjustments have to originate from.
With all that said, if you want to try and rule out a timing issue quickly, i'd just bump it to 20* initial and drive it "moderately" and see if the hesitation is better or goes away. If so, it's a timing issue....If not, we can look at the carb for the possible problem.
Sorry.....I said I didn't want to write a book, but the timing really has to be confirmed first.