do you think its possible to configure the BCR to control the Transpose parameter or any of these internal parameters? Or does this only work via sysex dump?

Unless I've missed something in the MX-8 manual, you can only change an MX-8 parameter via a SysEx dump of the complete active setup.
As described in the manual, a dump of the active setup consists of 91 bytes:
F0 00 00 07 0n 00 <parameters (83 bytes)> <checksum (1 byte)> F7

A "custom output" (".tx") definition of a BCR element (button/encoder) has room for up to 125 bytes (see "BC MIDI Implementation.pdf" (BCMI) section 14.6.6 for further details).
This is enough for a SysEx dump of the active setup of the MX-8, so a BCR encoder can control a single parameter of the MX-8's active setup.
For instance, a Transpose parameter can be controlled by the "val" data specifier (cf. BCMI section 14.6.1) in the custom output definition in the correct position in the SysEx message. (Actually there's a slight problem with the way the BCR displays negative Transpose values, but let's not worry about that right now.)
The MX-8 manual states that the checksum byte must be the "7-bit sum of dd..dd, 1's complement". I think this means that the checksum must be defined as "cks-1 6" (method 1, starting index 6); if this doesn't work, try "cks-2 6". (See BCMI section 14.6.3 for discussion of checksums.)

However, a big problem is that each BCR encoder only knows about its own "current value", not about the current values of other encoders. So the SysEx dump generated by a particular encoder always contains a MX-8 setup that is completely fixed except for the parameter being controlled by the encoder's own current value ("val"). Therefore it's impossible to control multiple MX-8 parameters independently via multiple encoders: turning one encoder always trashes any changes made previously via other encoders.