Drivetrain problem!

I have had issues with the drivetrain on my bike. I believe I’ve pinned it down to two issues.

1. The Shimano Deore XT SGS (long cage) 9 speed rear derailleur needs replacing. It was either damaged when off-roading or is just worn out.

2. The rear derailleur is designed to work with a maximum difference in the chainrings of 22 teeth. I have a triple chainset of 46-36-24. A difference of 24 teeth.

My question is:

1. Is it possible to replace my old Shimano Deore XT 9 speed rear derailleur with its 10-speed equivalent? Which is far easier to obtain. Would I have problems with the 9-speed chain passing through the cage? Can you see any other issues that might occur? One thing I’ve noticed is that the newer Shimano rear derailleurs don’t seem to have cable barrel adjustment on the derailleur and I don’t know how I will be able to make those finer adjustments to the shifting. My bike is old and has downtube shifters. 9 speed indexed for the rear and friction for the front derailleur.

I intend changing my 24 tooth chainring for a 26 and changing my cassette from 11-32 to 11-34. Hopefully leaving me with a similar range of gears. The Shimano rear derailleur I’m looking at is supposed to be able to handle up to a 36 tooth cog.

I don’t want to downgrade my componentry, but if your response is negative. I’ll either have to do that or move up to a 10-speed drivetrain.