First and foremost, Cockroach King immediately reminds me of Frank Zappa. He's a bit tough to get into, but has some great music. I recommend the album Joe's Garage.

Beardfish is another with a similar sound. Their album Sleeping in Traffic Pt. 2 is a good entry point.

The band with the hardest-to-search name, 3, is another good entry. Their album Wake Pig is a good'n.

Black Bonzo is somewhat similar. Any of their three albums is a good choice, but I'd suggest starting with Sound of the Apocalypse.

Bubblemath is a bit rough around the edges, and certainly more jazzy, but I'd be remiss if I didn't recommend what is, IMO, the best progressive jazz fusion album of all time, Edit Peptide.

Captain Squeegee is an odd mix of ska and prog that mostly falls a bit flat, but one of their albums is easily in my top 3: To the Bardos!

My "if I had to choose" favorite band, Echolyn, is the perfect blend of jazz, classical, and rock. Their album The End is Beautiful is a great entry point.

King Crimson, arguably the progenitor of all prog rock, is an important part of any prog fan's music library. Their debut album, In the Court of the Crimson King, is historically significant and just good music.