I have the
Sigma 300mm F/4 APO Macro and it was my go to astro lens until I got the SMC A* 400/2.8. This sigma is a good astro lens wants to be run at f/5.6 and if you look you might be able to steal one for the $130 I paid. When I was considering getting it I was hoping it would be a substantial improvement over my S-M-C 300/4 Takumar but didn't expect much at $130 but others said if I didn't like it I could probably flip it for about $400 to $500 so if I was paying somewhere in that range I could expect to come out even if I didn't like it. Well I like it and even though I don't use it much for astro anymore I still use it a lot.
I shot this
eclipse picture (this is a stack of 200+ that I should probably take another stab at processing) with that 300 at f/5
I also shot
this Andromeda image from my very light polluted backyard with that lens and the Hoya Red Intensifier on it.
If you wan to see what this lens does for other shots it seems I use it for a lot of my nature shots as all of the shots
in this album of mine was shot with it.
I thought I had an M42 shot with it as I know I took some but I may have flushed them once I got my 400.
As far as the Ultra-Achromatic-Takumar 300mm F5.6 goes, good luck finding one they are rare which also means expensive likely well outside your budget.
EDIT:
I still have some of my M42 shots with the Sigma 300 f/4 APO Macro and they are sharp enough but my editing ability has much improved from then to when I did the edits of M31 with that lens so that I don't want to show it. There are some nice crisp lines but man I crushed a lot of detail in the dark.