Get some flux core for the MIG..? A quality one, though; Miller or EWM - I only recently have come to appreciate the difference it makes.
For 2 x 2 angle I would use a stick welder. (What wall thickness?)
A Lidl or Aldi inverter would be plenty and as you say, useful for other jobs.
I think stick is better for something like this, rather than an under powered mig (if you have good fit up) having said that your mig should have more than enough power for the job.
Had some welding to do today and ran out of gas. I have a pub bottle and use co2. It's a bit of a hike to get it refilled and would have taken up most of the day but I have a spare co2 fire extinguisher so I took the nozzle off and the regulator fitted straight onto the bottle.
There are probably reasons why I shouldn't do this but it got me out of a hole hope it might help someone else.
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All the types of co2 bottle will freeze up if you are drawing a lot of gas or a long time from them.
Either dunk the whole thing in a bucket of warm water or aim a fan heater at the regulator.