I don't have a CNC, but a decent laser. This may be my disillusioned reason for no CNC (and space).
CNC's are messy and with budget machines with small beds, dust extraction and holding down parts for intricate work is a pain.
If you do choose the laser's dark side, before committing, at least look for budget options where you can cut around 6mm (or even add that extra .35mm and make it 1/4")... at least 3mm (+.175mm = 1/8") as you can always laminate (with dowel alignment).
An el-cheapo will char to engrave, however, a tad more powerful (
Splinter is the go-to-man) that can engrave to at least 1mm(+) depth will permit infilling for greater results.
Just remember that with either CNC or laser (or 3D printer), they don't just miraculously appear... you'll need to learn some design software.
If your first cut is too short... Take the second cut from the longer end... LBD