1. Fullrange speakers are great, don't underestimate them! The ones I looked at need some help at the low end, but you get away with a much lower crossover frequency compared to a tweeter. Since they can have a relatively big diameter (compared to tweeters) they have a stronger "beam"/focus; annoying when moving or having multiple listeners (off-axis sound is horrible), but for solo listening the stage/imaging gains a lot from not being disturbed by those pesky reflections.

2. Don't add a crossover if you don't have to. They mess with the phase at the crossover point and are hard to get right anyway. Just do it all in a DSP and have an amp for each speaker. You can actually combine room correction (often via parametric equalizer) and the crossover itself into one big FIR, if your DSP is big enough. You can also play with crossover frequencies, slope, sacrificing headroom for a deeper frequency response etc. - in the analog domain, the costs for the passive components quickly add up. That's why MiniDSP + array of amps can have a huge impact.

3. While I'd go with MDF any day, most designs will sound terrible without padding (or too much!). For your 3D printed design I'd expect proper padding to be the lower hanging fruit.

Anecdata: My 4" full range speakers are fully active stereo speakers: 4" FR + 4" woofer per cabinet (based on "Double Four", but with a different FR), 4 amps and an ADAU145x DSP for crossover & room correction (Beocreate 4). They play down to IIRC 40Hz (-3dB, or was it 0dB?) with ultra precise voice/instrument locations. (Not all that glitters is gold: IIRC they're limited to 92 or 95dB and I still need to redo the DRC since we moved).

Edit: For prototyping, there is the free Windows "Equalizer APO" I used to output the four channels using the onboard sound card and fed them into an older 5.1 receiver (with 5 integrated amps) connected to the speakers. That way I could rapidly swap the FIR filters and compare them to insanely large filters. This is nice for experimenting, and with a decent sound card can eliminate the need for a DSP when used to build dedicated PC speakers.