Front diff back lash - prop removal - R380

I have a late S3 with a 300TDi and R380. There is a lot of backlash in the front diff and a clonking sound when decelerating at under 10mph. It won’t clonk under hard braking or when accelerating. So, basically, when the pinion is unloaded the front prop shaft is flapping about. I can’t think of anything else.

Obviously I need to pull the diff out and re-shim the pinion but I have an MOT due this week and don’t have time to pull it out, order shims, re-assemble it (usually twice). MOT fail or not I’d rather not show up at the testing station with the drive train making funny noises so I’m thinking:

1, Take the prop shaft off at the front end and tap the end of the pinion forward with a club hammer to re-space it. Maybe some thicker diff oil?

2, Take the front prop shaft out and drive it with the diff lock on? This shouldn’t be a problem to and from the test but longer term is it an issue to drive around with the diff lock on & no prop? The wheels fore/aft will be able to turn at different speeds so it shouldn’t crab about.

I’m interested in your thoughts......

You seem quite certain its the diff but the front axle also has UJs at each end, all contributing to back lash.
If its that big an issue you may need to do a proper overhaul.
Surely its not an MOT issue.
I've driven with a prop off before, but only because of a prop UJ failure and only for a few miles. As you say, it will drive fine.

Thanks Bantam.
UJ are fine. There is about 30deg of backlash in the diff.

Is backlash checked by an MOT? Half the LRs on the roads would fail if it was.
Sounds like an advisory at worst to me.