Yep, pretty sure thats a MAK 90 (the thumb hole stock is a dead giveaway). I've owned a couple of them. They were produced from 1990 to 1994 and they were all modified (by Norinco) before they were allowed to be imported into the US due to the the old Assault Weapons ban that started in '89 IIRC. They weren't allowed to have screw on muzzle devices or a bayonet lug among other things.
I'll bet the reason that flash hider you have on it now is pinned on is the threads on the MAK 90's were mashed over to prevent being able to screw a normal flash hider/compensator unit. That one appears to slip over the barrel and is only held in place by that cross pin. It's most likely a mod that was done after it got here in the US by a previous owner if that firearm. I can't imagine it feels very stable with that setup and completely understand your displeasure with it.
Since the ban has expired, it's ok to fix the mashed up threads without breaking any laws. I've done it to my MAK the same way you're about to (tap & pilot) with no problems.
One thing to keep in mind is there is a spring loaded retaining pin (forward facing) in the front sight used to retain the flash hider/muzzle brakes that may be missing. Some of my MAK's had the pin just pushed into the front sight and then just peened in so it couldn't come out. The others were just missing the pin and spring altogether. The pin is pretty easy to make and even easier to just buy one, but where's the fun in that?
Shoot me a PM if you have any problems with it. I've built quite a few AK's and even hosted a couple of build parties when I was living in CO. FWIW: I've built from parts kits a Romanian AK47, a Polish AK47 sidefolder, a Bulgarian AK74, a Yugo M70 underfolder, a Yugo M72 RPK, and most recently a Yugo M76 (8mm Mauser
) sniper rifle. I didn't do too much with my MAK's apart from swapping the underfolder stock on one to a spare solid milled one and swapping the wood stock for a synthetic and fixing the muzzle threads on the other. I guess you could say I'm pretty familiar with them and their quirks. I still have quite a few kits and project guns set back for rainy days. I'm kinda waiting to see when I'll be opening up my gunsmith shop before I decide exactly what I want to do with them.
BTW: Here's how I would fix the sloppy feel. Cut the threads onto the muzzle with the die first. Then screw the new piece onto it hand tight and see where it bottoms out at. If you're lucky, the PWS logo and retaining pin notch "should" stop just barely before 12 o'clock (probably won't be though). If it's not, just remove the new part and chuck it up in a lathe with the threaded end facing out.
Here's a pic of the one I did for my M72 RPK:
Then take a few thousandths off the face and recheck it. The idea is to get it to where it turns by hand just ALMOST to 12 o'clock. When you put a wrench to it and tighten, then it should just stop at 12. Make sure the retaining pin I mentioned earlier lines up with the notch. It will be tight, have no slop and not be able to back out while the retaining pin has it locked. I do this on all my AK builds now. Even when using the factory muzzle devices. Works like a charm!