I was wondering what would happen if you gave a multimeter in the DC a super bumpy DC. The cap will definitely be helpful.

Multimeters use double slope integration AD conversion with relatively long times so are insensitive to the AC component on DC ranges. Some modern ones are using a sigma-delta AD with a digital decimation afterwards, which is generally a modern equivalent of good old integrating ADC.

But you never know how many corners are cut in a cheap design)

Again, do not leave the ampermeter load in this circuit disconnected even momentarily as this will fry the diodes and blow the capacitor. You may add a safety bypass of some kind (like ~5 pieces of 1N4007 diodes in series) if you can't be sure.

Yes, this bridge will work, though you should be careful with modern SMD parts as they get their cooling through the board mounting and when used in volume mount 'rat nest' circuit the cooling may be not adequate. Here the load is about 1/7 of max specified for the part, so you decide...

Also, it may be good to add an electrolytic capacitor to the circuit (any practical voltage you have on hand). Normally, a meter should suppress this, but some cheap ones may go mad about a little remaining HF in the DC current measured, why take a chance?

Would using this full bridge rectifier work? It's a Schottky-based type, so the recovery time should be really low.https://www.digikey.com/en/products/detail/bourns-inc/CD-HD201/6561443

Update: @RRK and @James: The thin arc of my lamp became unstable. It sometimes slightly moving and flickering. I can't capture this with my camera, because the tracklight must point down to ensure the tip at the top. I doubt if the arctube have cesium at all.

@James: And how the 6500K version reach Ra96 from Dy-Tl-Cs only? Other daylight rare-earths based on this chemistry, have lower CRI like the Osram HQI-BT 400W/D and its clones. It should have neodymium as well.
Looks like in the 3500K version, tin or other halide, filters the blue part of the spectrum to lower the CCT, and it also have brown vapor and afterglow.

Once I am settled down again I would love to *probably* trade away my 400W Diazotype MH lamp away to someone who will take care of it, I think you would be a good candidate for that. I just don’t really know what I should take for it.

I was wondering what would happen if you gave a multimeter in the DC a super bumpy DC. The cap will definitely be helpful.

Does Bosnia allow imports from China?, I bet the Chinese are still making thousands of them?
The repair thing is not possible with tungsten lamps as, even if you could somehow drill the glass bulb, you still need vacuum pumps and gassing machinery for the argon dosage!
I’ve seen crude lamps being made from jam jars using carbon wire and vacuuming it out, but these were just wacky experiments and didn’t tend to last long?

Also, it may be good to add an electrolytic capacitor to the circuit (any practical voltage you have on hand). Normally, a meter should suppress this, but some cheap ones may go mad about a little remaining HF in the DC current measured, why take a chance?

But if the intent is to run SOX lamp in spec, the current should be finally verified with said lamp fully run up, sure.
Though, 18W SOX is electrically close to 18/20W 600mm fluorescent.