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Did a quick search but couldn't find anything. Is the AVRI trem a direct replacement for the MIJ?

Mine's become really loose - both at holding the arm, and just the general feel of the thing doesn't fill me with confidence like it used to.

Cheers!

Yes, straight swap... I did it on mine.

I would say so. Put a mij one on my squier, but have heard of people putting usa ones on.

You can tighten thr collet though by gently squuezing it with some pliers (the bits on the inside that the bar slots into). I did this on my mij trem when i got it.

I swapped the trem of my CIJ JM for a US replacement with no problems at all as well. If anything it fits better because the string spacing at the tailpiece is the same as it is at the bridge.

If the AVRI fits, then the Classic Player trem should fit too. As long as you're changing, I'd suggest you consider that one.
If you put the proper spring under the screw-in CP trem arm, the arm will stay where you put it.

Use the plier method ONLY with the arm in the collet. Some have broken the collet by squeezing down too hard.

Another thing in to wrap a cable "ty-wrap" around the collet to snug them up. Leave it on, button it back up.