Destin,
I may have a solution for you in addition to the timing suggestions.
On my F135, I had a very similar problem to yours. Mine started when i took off my 1967 carb (with idle solonoid) and put on my blue window carb. I was wondering how on earth a rebuilt carb would cause this issue. I had no power off the line, but when the RPM's picked up it was ok.
I noticed on your two carbs (in the picture you had them side by side), you have different spacing on the lifter rod.
The lifter rod controls the throw on the plunger. This will make more sense by looking in a scanned section of the F engine manual. Figure 4-13:
Please then refer back to the picture youposted of the two carbs side by side you took earlier, and look closely at the lifter rod on the carb:
You have the one on the left "pinched" more than the one on the right. That lifter rod, when set incorrectly will cause the exact issue you are having because it's hooked to the bottom of the pump plunger (fig. 4-12) - which pumps fuel into your bowl.
In my situation, I had a perfect idle. But the second I gave it any gas - it was major hesitation and no power until i
SLOWLY opened up the throttle (not too cool if you just got a green light at an intersection).
Refering back to your photo's, again look at the one on the left. That one will plunge more fuel than the one on the right.
Now, you may be wondering how to adjust this. To adjust this, here is what you do:
I followed this from the F engine manual (from our era, the F135) and I never had the problem again.
Take into consideration I set everything as per the manual, and then I adjusted idle speed and mixture after that.
I hope this helps.
Good luck bud,
-dallas