I have an MET1; it uses 6 M8080s. The US version is indeed the 6C4, but that tube apparently was NOT designed for audio the way the M8080 is; the vast majority of 6C4s I bought, often by the half-dozens or dozens, were VERY microfonic and I tossed them. I did find some 6C4s--maybe 10% of those I bought--that were usable and I use them in the surround and SW channels, but you can't do that. Also, a 6135 is a heavy-duty version, and I have several--10 GEs and one Sylvania Gold Brand GB-6135. I have just 3 plainly labeled 6C4s, all RCAs. I kept one Philips 6C4WA and 3 Sylvania 6C4Ws. Do understand that this was from MANY-dozens of tubes.
...has a free tube-info app called TDSL. It indicates that 6C4s come in variants with 'P', 'P-EV', 'W', and 'WA' suffixes and also indicates that all the following are substitutes--CV-133, CV-852, EC90, and L77.
You can keep buying inexpensive 6C4s until you get enough to use, or you could just buy good M8080s from c-j.