Personally I combine a hash of something site-specific, eg. name, purpose etc and a base alphanumeric string. Allows each account have their own specific credentials while not being overly burdensome to remember.
> requiring you to use a very specific set of special characters?
Stupid requirements don't matter. If you have a secure password, e.g. a passphrase consisting of 7 random words (diceware) and the service complains that you're missing digits, uppercase, and symbols, then adding A0! to the passphrase does not make it less secure. Appending anything never makes it less secure. You can also write down in plain text and store on pastebin what you added per site because it's not part of the secret anyway. (Okay okay, might as well keep it private rather than pastebin; it's about the general point.)
> like 12 character max
This is not that common anymore, most services have reasonable limits. If you do run into one and it's too important not to use, then you don't have a choice anyway: you'll have to make an exception to the scheme and memorize or store an actual password for once. Doesn't mean you have to design all your other passwords for one exceptional case.
Ah, must've missed that you have an alphanumeric string. Mine had a couple symbols in it. I personally really like diceware passwords but the guesswork of "oh does this system have a 24 char max, does this one require special chars, etc" just got to be too much effort.
And while the 12 char max is (mostly) a thing of the past, I run into max char issues (usually around 24) far more than I should in 2021.