I admit I've never seen how loadings are southwards, but I've never seen them as bad as you describe. Often pretty full - yes, but not to the point that hundreds can't get on.
Never 100s left behind, even in the days last year of Northern never running Saturday services that didn't happen.
Like every TOC commuter time services are really busy part route in the rush hour.
At other times it can be really busy when events are on (Rugby at Murrayfield/Edinburgh Xmas market can cause crowding Lockerbie-Edinburgh, Manchester Christmas markets cause crowding Lancaster-Manchester etc)and during disruption.
As a rule of thumb the commuter busy services are:
From Oxford road to Preston usually the 16:10 & 17:10 Airport to Preston, 18:10 can have it's moments as well!
The 17:08 off Glasgow is busy with commuters going to Motherwell.
The 04:22 from Glasgow has some standing Preston to Manchester(07:47 at Preston)
Fridays afternoons and Sunday morning like every long distance TOC see busy trains, first two off Edinburgh in particular are very busy on a Sunday, possibly the busiest on the route as often full until Preston.
In terms of luggage so long as people bring the norm and the conductor manages the train well it's ok on Class 350s.
The Class 397s will be a huge help and much welcomed and it's good to see things moving as they become more familiar on the WCML on test/mileage/crew runs, won't be too long now.