If you use someone's composition and it's still in copyright, they're entitled to royalties. In addition, an arranger has copyright in their arrangement. So if you're playing someone else's arrangement there are two separate copyrights and two separate royalties.

It's up to the composer or arranger to decide whether they want to collect royalties themselves, collect them through an agency such as Harry Fox, or simply sell the rights to a publisher in return for a one-off payment.

With respect, I think you're making it difficult for yourself. I got mechanical copyright clearance from MCPS (the UK equivalent of Harry Fox) within a few days, simply by filling in the forms. It may rankle to go with the system, but the system is set up to deal with this, and they'll tell you very quickly whether or not the tracks are copyright and how much you'll have to pay. If you don't like it, then only record music which is out of copyright (although you'll probably still have to go through the process in order to satisfy the manufacturer)