As to what transport would be better than the MF CDP, that depends on your budget. The best transport for any sane money that I've heard--I now have two of them--is a Teac VRDS-25 or VRDS-25X with transport mods from ASE-Audiotuning in Germany.
The player will cost anywhere from $600 to $900, the new parts around $500, plus the cost, if any, of installation. The resulting transport is close in performance to my Esoteric P70 (retail: $7500), which is one of the best Redbook transports at any price.
Before doing anything, though, I'd ask John Wright if he recommends any player or transport as performing particularly well with the Meitner DAC. I've always found him an honest and fair-minded person.
Just my experience. I don't, however, use a Meitner DAC. Had a stock Bitstream years ago and found it smooth but bland. No experience with the modded version.
The Sony DVP-S7700, which you could pick up for $200, has a good reputation as a transport, even stock, but it's getting long in the tooth (2000) and Sony is not very good about keeping parts in stock (in contrast to Teac).
But by all means use your present player as the transport for a few months at least before spending more money.
Just my two cents' worth.