Remingtons are fine in my experience, especially the ones labeled "40% hotter." I've used Winchester Magnum, CCI, RWS and Remington No. 11s and never had a problem with any of them lighting real BP. I don't use BP substitutes in my sidelocks, though I've tried pyrodex in a Traditions Hawken Woodsman and it went off fine, too. Musket caps are unnecessary on a hunting sidelock, IMO.
If you want to go with musket caps, Schuetzen caps appear as hot as RWS and are usually readily available. I have about 1400 Schuetzen musket caps on hand and have used them in my Traditions Pursuit XT and they will light BP, loose Pyrodex and 777, and have not yet failed to light Pyrodex pellets and 777 pellets. They are good caps. Lots of compound in them. When I put them on the nipple, they won't go on as far as other caps I've tried due to all the compound in then. They stick out far enough off the nipple that they rub when closing the action. They make a helluva pop and will make a flame out of the muzzle. And they don't split wide open.
https://muzzle-loaders.com/collections/powder-primers/products/schuetzen-musket-capsI agree about CCI musket caps. The ones marked "Multiple Use" pretty much are the weakest caps going. They'll light real BP and loose pyrodex in my inline, but won't light pyrodex pellets reliably, and I think those pellets are actually pretty easy to light. They also split right open and loose a lot of its already inadequate flame outside the nipple.
Navy Arms used to sell muisket caps in its own tins. They were either "made in Germany" RWS caps, or "Made in Brazil" caps. I am not sure who made the Brazilian caps for Navy Arms, but those were very good, very hot caps. Not sure if they are still sold or not. But they shot a very nice flame out of the muzzle of my T/C Black Diamond.