if this is a points ignition: i know you checked timing, but did you check dwell?
if the dwell is out of wack then when you rev the motor the engine timing can go anywhere, it could be fine at low rpms but the minute you rev it the contacts could go totally out of alignment or the timing could increase too much on top of the mechanical advance.
something else could be a problem with the vacuum advance. the diaphragm might of blown. that would cause a vacuum leak only off idle.
the cars used ported timing, that means at idle your working off the mechanical advance only and vacuum at the advance is 0HG.
the second you come off idle the vacuum advance comes on.
does it backfire if you slowly raise the throttle?
try plugging the vacuum advance as a test and blip the throttle and see if the backfire stops.
If you are running points i highly recommend changing to electronic ignition.
the problem is today the replacement condensers and points are all made in china and complete JUNK!
the vintage stuff from the 1970s or 80s is the only good stuff left and you just can't buy it outside of ebay or a swap meet.
as a real life example i ran points back in 2005 every 100 miles i would come back and check timing, the timing was good, but the dwell was WAY out of spec, i would readjust the points and the dwell was perfect, 100 miles later and again the dwell was out of wack completely the point of contact wasn't even wearing on the distributor cam it was like the spring was getting weaker and weaker on the points and the car would misfire when accelerating. i changed to electronic and while i had major issues at the start overall the reliability is much higher.
long short,,,, check dwell if you have points and the timing is correct.
inspect the accelerator pump just in case.
try pluging the vacuum advance and see what happens.
besides taking the carb apart and inspecting you start getting into swaping parts till you find the problem.
Condenser and coil swap out first, then wires and if you do the wires inspect the plugs see what they look like and the gapping on the plugs needs to be checked.
there are more things that it could be.
you also don't want to start chasing your tail,,, you do all the work only to find out the gas went bad..... when you put the car to sleep did you put stabil in the fuel tank?
I had one car i poured stabil in the tank,, in the spring the car ran horrible i pulled the plugs and the porcelain on every plug was PINK!!!! changed all 8 plugs and dumped the fuel in the tank, problem solved. I learned new ethanol 10% gas takes a long time to go bad and there is no need for a winter additive, just fill it up and cap the tank good for months of storage.