I have a 3 in 1 multiprocess Miller 220, I'm very happy with it. Multiprocess is great if space is an issue, I have a very small shop so this is a great machine for me. It was also a pretty good deal, as I could not have bought an equally capable combination of Miller MIG, TIG and stick machines for the price.
The closest comparison I can find in two machines is the Miller 211 (MIG) and Diversion 180 (AC/DC TIG) and that works out to about $2600, vs $3000, is not stick capable and has slightly inferior TIG capacity (180A @10% on the Diversion vs 210A @20% on the 220).
Not really familiar with ESAB but from reviews their 205 is very similar to the Miller 220, better in some ways, not quite as good in others.
A big advantage to multiple machines is you can get exactly what you want and upgrade either independently. Since you already have a MIG that meets your needs, you can spend less and still get a pretty good TIG, or spend around the same as a multiprocess and get a really good TIG (better than what you get in a multi-process).
Later you can upgrade to a better MIG, again spending less for similar performance or getting a better MIG than what you get in a multi process.
As mentioned there are a lot of cheap TIG machines right now if you get away from the big names, and some are getting good reviews.
There is a guy in my welding class who bought a Harbor Freight DC TIG welder that works well enough for his needs. It cost less than $700 or about 1/2 the cheapest TIG welder from Hobart, Miller or Lincoln (although they are not even close to an apples to apples comparison since all three name brand machines have superior specs to the HF).
As far as your brand preferences, Lincoln does not currently offer an AC DC TIG, MIG, Stick, only the 210MP which is DC TIG, MIG, Stick so no TIG welding aluminum. I'm not familiar with Forney and didn't look at any of their machines when I was shopping for mine.