There should be spots available. The training provider now has an entire campus in TX (which has grown from a three plane operation to a fleet of 40-ish aircraft) devoted solely to RTP training. Every student there is an Envoy RTP candidate. I think most information about the backlog are from when they were starting and growing that operation.

It may depend on what length of program you need. Time-building is likely easy to accommodate. Every flight school gets a bit capacity constrained in multi-programs (due to fewer aircraft). Write [email protected] and get the current projected start dates from the recruiters.