I know the parent case for all 3 of them is the .220 Russian, but I would start with a 6.5 Grendel version. You can use the mags and everything. You’ll only have to swap the barrel, and feeding will be proper, since 6 ARC was designed off the 6.5 Grendel, and is very similar in size, shape, and dimensions.
Also, I don’t know about the Rugers, but AR’s have a Grendel 1 (7.62x39) and Grendel 2 (6.5G specific) type chambers, with the Grendel 2 having become the standard. The bolt face depth is different in them. This is why I say start with a 6.5G rifle. Plus the other reasons I mentioned.