as the title says, engine #2 shuts down when tanks 2l/r are close to empty (<0.2t) even when crossfeed valves are open, turning off tank 2 fuel pumps seems to somewhat mitigate the issue

I ran into a similar mismanagement 🙂

You need to manage the fuel load so that tanks 1, 3 and 2L/R are equal.
If there is a greater fuel load than tank 2L/R capacity, then you need to turn off 2L/R and feed ENG 2 from 1 and 3 (including using 1A and 3A accordingly to feed tanks 1 and 3) untill the fuel load of 1 and 3 is equal to 2L/R, then you can feed from all at once.
Cycling the crossfeed valves before turning off any fuel pumps is a good idea to make sure that they are definatley open.

Essensially if everything is right and you have a low fuel situation in 2L/R, then you should also be low fuel in 1 and 3.. which sounds like an emergency. 

See the manual reference below. 




Check out page 76 
https://forum.inibuilds.com/applications/core/interface/file/attachment.php?id=25570&key=7bd0b1032193c7941af5a613dac51bf6