Answers based on unverified information from various sources (at a time I thought the 2H was what I would get next) as I never had any 2H chips (sold only in Europe).
Although according to bith FM and my parallel programmer the chip is set to x12, it is in actual fact running at a x6 clock.
The RX2 defaults to 12X, the older RX2H defaults to 6x.

I also tried to set the CKCON bits to achieve x12 clock compatibility for my timers and UART, but that doesn't seem to work either.
The CKCON register does not exist in the 2H

Erik