So, It's now clear to me that not all STC's are created and used in the exact same way. Yes, you must have permission (letter of authorization), but some of the STCs grant that permission through a generic letter that you can use with the purchase of a kit - which after talking to a local IA had no problem filing the STC with only the STC documentation provided by Parker Hanneflin here:
https://www.parker.com/parkerimages... Brake Division/Kit Documents/199-62A Kit.pdf
Basically the LOA says if you purchase the kit (199-62A) then you have approval to install it and file a 337. I didn't have to purchase the STC directly - just as though you can buy the 199-62A through Aircraft Spruce. Just for good measure, I called the Parker technical support hotline to ask if I needed to, or what the process was to purchase the permission letter signed specific to my aircraft. They never called me back.
Here is exactly what the LOA in the STC says:
So there are IAs that can interject their own interpretation here. Just goes to show you need to shop around to find an IA that understand this. But it seems that anyone can buy a 199-62A kit, new or used, from Parker or ABI since it's a PMA'd replacement for the Parker kit - it's exactly the same. So basically the STC is free to use if you've purchased the kit - which you will have done if it's in your possession. Someone can try and tell you that you need a signed letter from Parker - but they don't give you that - they give you this blank, generic LOA. This is all you should need.
This should work, even for the 185F. This has been a discussion point for a long time on the forums. SA63GL is basically free seems to be the consensus. It really shouldn't be this hard, or this confusing. Anyway, this is what I just did - and I know others have done.