I didnt know there was a TPE south?
IMHO the Manchester Airport - Cleethorpes service has nothing to do with other TPE services (even calling it "TPE South" seems a bit false, but that's the timetable description it got); it was added to the franchise to beef it up, but would fit better with EMT or maybe even Northern would be better than TPE.
Newcastle - Carlisle or York - Blackpool cross the Pennines but aren't part of "Transpennine", so I'm not sure why the Cleethorpes service is (it serves Manchester Airport, as a lot of TPE services do, but then so does Southport - MIA and Liverpool - MIA and MIA - Crewe!)
EMT running liverpool to norwich is a strange one as it really out of their region mostly
It's a hard service as it's not really in anyone's "area". EMT do serve Sheffield, Nottingham, Grantham and Peterborough, so there's some logic to it being with them.
One trouble with it (other than train length, bottlenecks etc) is whether it's better to run it from the middle or from each end. As EMT are running it from the middle, they don't have the resources at Liverpool or Norwich (so early/ late services don't go "full route" and trips are often capped before getting to the terminus if things go wrong).
Here in South Yorkshire the Sheffield - Rotherham - Doncaster bus service used to be jointly operated from Sheffield and Doncaster depots. Now, it's 99% run from Rotherham, which gives some benefits but a lot of disadvantages.
If the Liverpool - Norwich service was run as a joint Northern/ NXEA service then it would solve a lot of problems (but create others!)