Have you thought of trying a fight pad instead? Probably way more in line with your budget for a quality one. Hori makes good stuff. The Fighting Commander 4 was great and they just released its successor on Xbox S/X so hopefully it'll come to PS5 soon.
https://www.amazon.com/dp/B08NDT2CGS/ref=cm_sw_r_cp_apa_glt_fabc_GDKMTN1E3ERZJF94XMCN
The white Hori Fight Commander for XB1/PC has been replaced with a new one for Xbox Series X/S and it's now in a black finish. I just had to replace my OG Fighting Commander and got the new one a few weeks ago. I'll just say i liked the feeling of the dpad on the OG model... But the link is below:
It the Hori Fighting Commander OCTA. I use it too. It is superb.
Hori Fighting Commander Octa Designed for Xbox Series X|S By - Officially Licensed by Microsoft - Xbox Series X https://www.amazon.com/dp/B08NDT2CGS/ref=cm_sw_r_awdo_9AH3B9FF24166QR2BN8Y
I think the Playstation Version will be released in a few Month
I just yesterday received a notification from Amazon that it's available to order NOW with the usual delivery timeframe (2-3 days).
Currently I'm waiting for the first reviews to pop up before I give it a try.
I just happened to see this thing called fighting commander OCTA controller for Xbox..release date April 30....not sure if this is related to our OCTA...
https://www.amazon.ca/HORI-Fighting-Commander-OCTA-Designed/dp/B08NDT2CGS
New Hori is coming out March 29th, just wait
Hori Fighting Commander Octa Designed for Xbox Series X|S By - Officially Licensed by Microsoft - Xbox Series X https://www.amazon.com/dp/B08NDT2CGS/ref=cm_sw_r_cp_api_glc_fabc_VMWJMG5XKNXBZTXE0RR0
I use Hori fighting Comander Octa it really helped with analog direction imput in this game.
Thinking out of the box here, what if you used the board and buttons from this here. They are microswitch buttons with built in springs. : https://www.amazon.com/Hori-Fighting-Commander-Octa-Designed-x/dp/B08NDT2CGS
I got this https://www.amazon.com/gp/product/B08NDT2CGS/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
since it was recommended.
The stick on this is more precise since it has gates and I found that much more usable than a regular xbox controller stick/d-pad.
I've seen many complaints about build quality of OCTA. If you take a look at reviews on Amazon there are lots of people who had shoulder buttons come off. Comparing OCTA customer ratings to Hori Fighting Commander you can see that OCTA is really rated low.
I personally have Hori Fighting Commander 5 (the last one before OCTA was released) and it's the best controller I ever had, in particular the D-pad quality. I was set on getting OCTA but reading reviews on the internet I can't resist an impression that it is a huge step down compared to its predecessor. Also, the fact that it requires (Windows only) software to get access to all its features is a dealbreaker for me.
You could give the Hori Fighting Commander Octa a go.
I haven't tried in myself, so can't personally vouch for it, but it looks nice.
https://www.amazon.com/dp/B08NDT2CGS/ref=cm_sw_r_tw_dp_R7H21QZK37Y73187Z43H