I look at most of these as just places to take your money.
It's like the APR and CKC in the dog registeries.
They take your registration fee, do a couple of shows but in general are not recognized by the public as a registry to add value to your horse. Especially when in their question and answer they are allowing a mixture of breeds.
It also doesn't seem to be requiring anything to certify in gait.
But overall it's your dollar, just realize that if you ever have to sell most will still consider the horse a grade if they aren't with any of the more recognized breed registeries.
If your mare is/was registered isn't there a way you could appendix the baby into the Foxtrotter Association? Like they do with the half arabs?