They(stahlwerk) do an AC/DC tig inverter for not much money, one model with a built in plasma cutter. I have used one and they are not bad at all. The only issue is you cannot use a foot pedal when welding.
https://www.stahlwerk-schweissgeraete.de/en/TIG-AC/DC-Welders/AC/DC-TIG-200-ST-IGBT-Pulse.html
Wonder what will happen to the price after 31st.
Just looked at the link and their english seems to have taken a turn for the worse.. Used to be better.