If you genuinely feel that you'd rather have a Parker Reproduction 16-ga. set of barrels than a CSMC RBL 16 then, by God, that's what you should get.
16-ga. Repro barrel sets by themselves do become available from time-to-time, but very rarely. You may look a long time to find a set -- perhaps a year or more. What might be a better option for you is to trade in or sell outright your present 20-ga. Repro for an original 20/16 Repro bi-gauge set -- they come to market quite frequently. There would be no worries of the barrels fitting properly and the original bi-gauge set, I'm quite sure, would be a better investment, holding its value, maybe even appreciating than a cobbled together set.
One thing is certain -- if you would go the original bi-gauge route and make the deal a single set of 16-ga. barrels will become available within days.