What you're looking for is lower latency, not bandwidth.
Unfortunately network latency likely isn't the biggest delay here.... unless you've got a lot of switches between your units or networking problems.
It takes a certain amount of time for each step: for the channel change command to be received by the mini, processed, then sent over the wire, processed along with everything else the Premier/Roamio is doing, the tuner instructed to change channels, waiting for channel lock, then waiting for the video stream to be processed/packaged up for xfer over the wire, then transmitted back to the mini over the wire, video is processed/decompressed, then sent over hdmi , processed by the tv and then finally put on the screen.
Software updates probably will help on a couple of these steps to shave off a millisecond or two here and there once optimizations for the new generation of hardware are all in place... but dont expect miracles.
For an example of signs of optimizations, see how trick play works much smoother, with a higher framerate with the new software (20.3.7) when viewing shows via MRS, even with a Premier as the sender.
Bottom line is that more lanes on a highway thats already about 5x wider at 100mbs than it needs to be to xfer the video stream isnt going to help much.
-Roamio Pro/Slide Pro
-Comcast/TiVo Mutant dvrs - RIP
-2x Upgraded Series 2 - Retired