Sounds like most of the normal items have been done but obviously haven't cured it.
The pressure and vac check should immediately tell you if the crank seals are bad or on the way out - did you see this being done?
The pressure and vac test will also tell you if the impulse line or carb boot is holed, if the test has been done correctly, the saw should be air tight - did the tester move the crank shaft round whilst the saw was being checked? This should be done to fully test the seals.
From your video, it looks like the saw when in the felling position, runs out of fuel and then, when trying to start it, it doesn't start right away like a warm or hot saw should. When hot, does the saw start right away on the first pull?
One thought is that the fuel line is non standard and is shoving the fuel filter in to the filler end of the fuel tank so when on its side, it dies - well worth a check.
My other thought is to let the saw die in the felling position and then strip the carb down immediately and see where the fuel is in the carb - pumping section, diaphragm or neither! Worth checking the colour of the plug and if it is wet or dry as well.
Are the AV mounts OK? I once had a Husky that would over rev when held downward and it was shot AV mounts but think probably not!
I have heard of the crank seals having this effect but it usually manifests itself as poor idleing and over revving.
IMO, it looks fuel related and looks like it runs out of fuel.
Where about's in the country are you, I do one or two saw repairs for members who have run out of patience, luck and usually pick up the problems no one else has fixed or want - story of my life:001_rolleyes: you may find one of the other guys/sponsors are local to you and can assist!
Let us know how you get on!