Your tractor specs out at less than 20PTO HP and only 26 engine HP.
TractorData.com Kubota B265 tractor information
You're asking a lot for 26HP to move 4500# up that slope AND run a 6' mower and trying to maintain speed.
The general rule of thumb for brush cutters is 5hp per foot, or so I've read here on TBN many times(don't know if its true or not). A 6' brush cutter would require 30PTO HP if it is true. Don't know how that equates to finish mower.
Landpride lists your mower at up to 50HP, but lists no minimum HP requirement.
https://www.landpride.com/ari/attach/lp/public/specs/310-262s.pdf
Here's a link to an old thread by Island Tractor addressing HP and mower width. Good discussion.
http://www.tractorbynet.com/forums/attachments/96404-72-finish-mower-21hp-tractor.html
Can you do another video, following the same path, using the same ranges, with the PTO off, so we can hear the engine/tranny strain without the mower running?
With all that said, I'm very surprised that when you switch from M to L that it doesn't just walk right up that hill. Really surprised that it was just as weak.
Maybe something's wrong with the machine. Maybe there's some obstruction in your HST that isn't allowing it to get full flow? Maybe a faulty filter or screen that's installed incorrectly or backwards or some idiot left a plastic sheet on, etc...?
I'd ask the dealer to take a look at your video and see what they think. And I'd ask if they have a 5' used mower that you can test-drive.
Good luck. I'd hope it's something mechanical that is an easy fix. It just doesn't sound right.
My little PT425 is all hydraulic and I'd expect noises like that on a slope with the finish mower running too, but by letting off the pedal like you did, it should have enough power to go up the hill slowly while maintains the PTO speed.
I'd lean towards your gut feeling and think something's not right, but again, that's not much HP to move that weight and keep that much mower spinning. The grass doesn't look long, either. Once it gets taller, you'll only be able to mow downhill, shut off the PTO, drive up, turn on the PTO again, etc...
Get the dealer involved.
Sorry for the ramble. Good luck and keep us updated.