Nice build

1,2kHz, that's low, I crossed at 2, but the difference definitely is the size of the woofer, mine was a 5" in a 3 way design.
I followed the works of Heissmann acoustics:
https://heissmann-acoustics.de/en/test-seas-dxt-27tbcd-g/
Here he describes how the little DXT waveguide, works best if put in either a very narrow or very wide baffle - also seen in Kii3 and Grimm Audio.
I used it with an SB MW13TX in a very shallow cabinet with slanted cuts like yours too, giving me a smooth and even response both on and off axis.
Another reason I asked, is that I've seen so much praise given to specific equipment, when in fact it's most likely a dispersion, frequency response or something else related to the overall response, rather than "fancier" gear. So if you like your speakers, and they do the job, just juice up the amp for the woofer and be going - unless you really really want to fiddle with FIR - which might just give you more latency - which again is something rarely desirable in mixing/studio - AFAIK.
Definitely listen carefully to Keith_W - he has a great point in his post - especially regarding FIR being a nice to have or need to have.
Give Fouraudio a look... they use pascal amps and have DSP too - with FIR. Genuine Audio uses them:
https://www.genuin-audio.de/en/produkte/neo/
I think a powerful 2 way plate amp should be within your price range - unless you really want to have something separate.
By the way, do you have measurement equipment, which? and how do you measure when making the filter in your speakers?