The OD on K, L and M are all the same. It's the ID that gets slightly smaller with the thicker wall. Don't use the M, it's about as thick as tinfoil.
I haven't seen any thick-wall fittings but then I didn't worry about it. The "normal" plumbing and big-box store fittings are fine!
I have run my (soldered) 1" type L system at 140 psi for years with no problems.
