The acceleration pump should only work when twisting the throttle, it helps avoid the stumble when taking off. I am backfiring(popping) on hard DEcelleration which is an indication of a lean idle circuit.
or an exhaust leak, especially where the pipe joins the head
or one or more exhaust valves too tight (not closing fully)
or there is one or more vacuum leaks at the manifold boots (between the carbs and head)
Three turns out is a lot. If the carb to head rubber boots are very hard I would suggest replacing them as a means to remove the possibility of vacuum leaks. If none of these correct the issue then I would suggest a more careful inspection and thorough cleaning of the carbs. People bash the later PD "keyhole" carbs but I have had good results with them. I am running the flat top 836cc (65mm) cruzinimage pistons, a CX-1 (Web Cam 41) cam, K&N filter in the stock airbox, and a MAC 4 into 1 header with a straight through baffle. I started with 125 mains and mine fell on its face at 5000rpm when the main fuel circuit would come in fully. I ended up reverting back to 110 mains with stock idle jets, idle mixture screws 1-1/2 turns out, carbs carefully synchronized, and am still showing a slightly rich condition. This is on my Street E/T dragbike that spends most of its time between 7500 and 9200rpm with a Dyna S ignition, Dyna 3ohm coils, and Denso X24ES-U plugs to light the mixture.
I did use one shim under the main jet needles (equivalent to about half a notch) when I installed the CX-1 cam to bring the main jet circuit in just a little sooner.