best bass or close to that 12AX7 tube

I have tube swapped now a fair amount (on an Ayon CD player and an Ayon integrated). From this and reading what others in their systems say when they swap out tubes like I have is that, generally, the effect of tube swapping is highly variable on the system... and the perceived sonic benefits and demerits of the swap are also very dependent upon the persons personal tastes. So... the only reliable way to swap tubes is trial and error in your system.

For what it is worth, there are some generalities in 12 AU7's that seem to be applicable in many systems --- RCA tubes are more punchy and have slightly better bass than Mullards but are brighter and have more sibilants. Mullards are warmer, smoother, less bright, less punchy with less well-controlled bass. That said, there is variability in RCA's when compared to other RCA's --- though Mullards seem to be very similar across varied stock of Mullards.

So... again -- you are stuck making a purchase and hoping for the best. I contend that none of us out here with different systems and different ears can help you much.

FWIW, I chose for my system the Mullards over the RCA's because I like the smoother rounded-off sound that takes the edge off certain piano, violin, and clarinet passages. The Mullards made some strident recordings (of great music) listenable --- where the RCA's were too bright and etchy. Yes... I do prefer the better bass control and energy of the RCA's over the Mullards... but based upon my listening preferences the trade-offs with the Mullards worked better for me.

Given your price range, you might want to try the Psvane tubes --- I have not heard them, but they are supposed to be great --- if you do try them let me know what you think.