Can this work? I tried setting up a SRAM Rival double FD with a SRAM XX 42/28T double crankset and while there is enough swing for the mech to reach both rings if the limit screws are set right, the double tap shifter's pull doesn't seem to be enough-- shifting can't get the chain off the small ring. Is this a typical incompatibility between SRAM road and mtn comps?

If I replace the Rival FD with a X7/X9/X0/etc will that solve the problem? Will it be compatible with the doubletap shifter? I'm new to SRAM and was under the impression that their road and mtn groups were mostly interchangeable.

Also, the front doubletap shifter is really hard to activate and makes a violent bang when releasing cable tension (moving toward the small ring). The rear shifter feels as I would suspect, similar in force and feel to Shimano. Is this normal?

IdK , cant see it working in front of me. Visit an LBS, probably in the spring when your Drifting snow Melts.

I'm not familiar with SRAM's road/MTB compatibility but I do know Shimano's MTB and road front derailleurs aren't compatible with each other's shifters so it wouldn't be surprising if SRAM's aren't either so replacing the Rival with an XX may not help. Also a road front derailleur will have a cage curvature matched to a 50T or larger big chainring and your 42/28 chainrings are awfully far from that design.

Since you are using a road derailleur with road shifters I would expect it to work.

When the chain is on the small chainring, do you have all of the cable slack out? Cable should just be loose enough to allow the derailleur to bottom out on the limit screw.
The hard action and bang when shifting down is likely from having the upper limit screw too tight - you have too much tension on the cable.
I think I'd try things with the limit screws wound back to ensure you are getting the maximum travel available.

Have you tried loosening the high-limit screw slightly? Perhaps it needs to overshoot the big ring a little to shift, and you're preventing it from moving far enough with the stop. I'd probably let it out until it overshoots and throws the chain off to the outside, then try to bring it back in until everything works.

Interestingly, I've taken the high limit screw completely out to allow the cage to move past the large ring, but the shifter itself does not move the derailleur that far. I've adjusted the tension on the cable such that when the mech is at rest at its low limit (set by the low limit screw), the tension in the cable is minimum, not enough to prevent the mech from hitting the limit screw but high enough that any shifter movement moves the mech instead of taking up cable slack.

I'm really thinking that the shifter isn't pulling enough, and this may have to do with the shape of the cage not matching the small (42T) large ring arc diameter well. It may be that with the non-optimized cage shape more pull is required to trigger the derailment. If it were a friction shifter or a micro-adjusting brifter like Shimano's where you can manually trim, it would work just fine. But with SRAM's pseudo-indexing on the front, it's no dice. It moves one distance, no less, no more. Bummer.

As for the difficult shifter action, it's weird-- it has nothing to do with the limit screws restricting the movement of the derailleur. It seems to have everything to do with the pivot geometry and/or spring tension, since there is still travel left in the derailleur when the shifter is set to the large ring. But then "tapping" to release feels like a huge amount of tension is being released in a sudden burst. Way more than in a similar Shimano brifter setup that I have on another bike.