@EmeriousNineHi again - sorry to hear it is still not working. One of the problems in helping you to get a solution is the variety of PC setups/Windows versions. Sometimes what works for one doesn't for another.
When the game crashes to desktop, do the following: Windows key+R, type in "Perfmon /rel" when the page comes up, take a screenshot. You will see red dots(Critical events), blue dots (information) and yellow triangles (Warnings). Click on the critical dot on the relevant date of the crash and look for anything that references to Star Wars BF II or Origin. If you find any Click on VIEW TECHNICAL DETAILS and take another screenshot. Do the same for Warnings. Post screenshots here.
Other things that you can do is Turn off the Origin in game overlay and cloud saves in Origin application settings. Also turn on FPS and position/size to your comfort. Watch to see of the FPS gets too low before crashing.
Also Did you update Windows Version and have you disabled Directx 12? For Directx12, go to your documents/Star Wars Battlefront II/settings folder, Open Bootoptions file with notepad. 1st line should be " GstRender.EnableDx12 0", If it is just close, if not change the 1 to 0 and save.
The silly thing is that I can run every mode of the game on my PC without any problems others are having and I have a below minimum spec graphic card (GTX560). I can't even replicate your problems so I can see what's happening.