I'd choose to remove the inner timing cover, then remove the pump. Technically the crank pump gear should be removed to take the pump out, but the shortcut is unscrewing fixing studs. If you want to remove the pump gear, remember the crankshaft has counter-clock threads!
Comments about removing oilpump:
http://www.a7a10.net/BSA/Oilpump.htmCan be done by removing 3 nuts & the two lower studs (carefully, do not destroy threads). This makes it possible to get the pump out without having to disturb the crankshaft driving pinion. To prevent all the oil spilling out you can plug the feed holes while working, or do the work in conjunction with an oil change. Check or change the gasket at the back of the pump, & remember the small gasket at the front stud or you may bend the pump's housing when tightening the nut.
To check play, a tyre lever (or something like that) carefully under the pinion, and watch\feel whats going on. My impression, if you even see\hear\feel movemnet, then it's time to do something, others here may come up with what's admissible.
btw, any tiny powdery non-magnetic residues in the oil? (for example from small end bushes, also a possible cause of noise).
Hoping some of this is useful. Good luck.