Update:

I’ve been able to get ‘Fire Weapons’ mapped to LMB using a handy tool called X-Mouse Button Control.

I’ve also managed to get Mouse Move working on RMB with one hitch. Whenever I fire using LMB (which should just be sending a keystroke bound to ‘Fire Weapons’ ) the game detects the keystroke AS WELL AS a LMB press, which will then disable my Mouse Movement and I have to press RMB again to re-engage it.

So my workaround is to just stay in mouse flight mode I guess. At least I can fire with LMB.

Here is my X-Mouse Button Control setup to achieve this if anyone’s interested: