Wow .............. Randy, you and I use(d) the same equipment and we have the identical problem.
I kid you not - it sounds like you were watching my machine!
I'm running a Lee undersize die as well as a DAA Mr Bulletfeeder for 40S&W.
I also have/had the double "thump/pop" on the upstroke as the toolhead was rising.
(1) I swapped out the DAA Mr Bulletfeeder powder funnel and went back to the old/original Dillon powder funnel.
It fixed and totally removed "one" of the two thump/pops.
I worked hard at setting the depth of the size of the bell/flare and I made it as minimal as possible - to the point that the bullets wouldn't actually sit in the casing anymore and would fall out.
Even with insufficient flare/bell, there was still a "pop/thump" as the powder funnel exited out the top of the case on the upstroke.
There is binding using this DAA powder funnel regardless of the depth you set it to.
One can readily see that the DAA Mr Bulletfeeder powder funnel for 40S&W has a distinct and visible "ridge" on it so that the bell will appear to be slightly less curved.
The plain Dillon powder funnel is smooth and curved giving a more pronounced flare.
Once again, I set the original Dillon powder funnel to provide the minimal amount or bell/flare where the case would still accept the bullets from the feeder in the press.
The "pop/thump" has gone with the re-installation of a regular Dillon powder funnel (the plain old "W" sized 40S&W/10mm powder funnel).
(2) I'm running cleaned, de-primed and roller re-sized, mixed range brass through my 1050.
I also use the minimal amount of case lube on the brass as well.
I notice on the upstroke that just as the Lee undersize die exits the top (lets go of) the casing, I get a "pop/thump".
No amount of additional case lube has been able to remove that thumping - it does reduce it a little.
I've also tightened down the shellplate so that it has little, very little vertical movement, and I installed a low mass ball and ring bearing from Hit Factor Shooting.
The shellplate travels smoothly around the press, and a snug shellplate makes resolves any case feeding issues from the little shuttle into the shellplate.
The swaging station also doesn't create any resistance, binding or popping.
BUT, I haven't yet managed to remove that "pop/thump" as the Lee die comes off the brass on the upstroke.
I'm reluctant to get rid of the Lee undersize die ........ but it seems I may have little to no choice.
Randy:
Did you get rid of your Lee undersize die?
Did it get rid of the pop/thump?
Cheers