The fact that your hammer is pushing them down enough on the first strike and finally making them close/tight enough to actually fire on the second is the give away... Make sure they fit good, then seat them WELL... Not OVER hard, but right..
This could be the problem, but the OP says that with his light mainspring, and even with all types of #11 caps, he gets misfires. As most know, CCI #11 caps will stay put on nipples where a Remington #10 fits snugly, but only if you pinch them a bit oval shaped. However, it's just the edge of the cap that is gripping the nipple and it takes very, very little pressure for the hammer to fully seat them, even if you don't seat them with a dowel.
So, I would think that these at least should have fired reliably on the first strike, if it was just an issue of the hammer striking force being reduced by having to fully seat the cap on the first strike.
I use CCI #11 caps pretty much exclusively right now, and as I mentioned, my Pietta Remington (which is supposed to use Remington #10 caps) has a lightened mainspring that I reduced in thickness with emery cloth. I am getting pretty much 100% reliable ignition ( so far) and I don't bother to use the dowel to seat them.
Without being able to try the OP's R & S in person, I don't know how much pressure his lightened mainspring has compared to mine.
But, I suspect it's less, and this may be the problem.