"I also need to check the adjustment of the transmission kickdown (I don't think this would affect starting from a full stop).  

When I got the car the trans kickdown didn't work at all.  I got it to work by trial and error but I recently found the instructions how to do it correctly."

The TV LINKAGE has to be adjusted with a fluid pressure gauge (see correct year WSM). There is no ands, buts, ifs or maybes.

Also correct band adjustments.

It sounds like your problem(s) is mainly the LOAD-O-MATIC and the TV LINKAGE. You need to go to a DUAL-ADVANCE DIST.

Make sure all of the TV LINKAGE is not worn and any bushings are good. Engine mounts also. If the engine moves on torque application it will negate any adjustment.

The reason(s) for the single range in those years was fuel economy (2nd gear start) and to compete with the scrub POWER-GLIDE.

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Common sense tells me that more fuel would be required to get a car moving from a dead stop in 2nd gear because it doesn't have the advantage of the torque multiplication of low gear. If the transmission valve body, etc. are such that a transmission will automatically shift from low to second at a low rpm, it should only remain in low just long enough to get the vehicle moving. For example, my truck has an 8-speed transmission with a 3.92 axle ratio. It always starts off in 1st/low gear. With a gentle touch on the pedal, it will be in 5th gear by the time I reach 20-25 mph. If there were an mpg advantage to starting off in 2nd, surely the transmission could have been programmed for that.  

I found the problem causing the hesitation (after tearing into the carb a few times), fuel cap was not vented.   The cap that came with the car was old, I thought it could be the original, so when I replaced the fuel tank I decided to use the old cap.  I bought a new vented cap from Rockauto and the hesitation/bog is gone.

56 Vic, B'Ville 200 MPH Club Member, So Cal.