Since we can't agree on a single ideal reference UTM, we instead approximate it by limiting ourselves to a class of "natural" UTMs which are mutually interpretable within a constant.

Even if you do that, you're left with an infinite number of cliques such that within any given clique the languages can write short interpreters for each other. Picking one of the cliques is just as arbitrary as picking a single language to begin with. i.e. for any given class of what-we-intuitively-think-of-as-complicated programs X, you can design a language that can concisely represent members of X and can concisely represent interpreters with this special case.

What I'm confused about is this constant penalty. Is it just "some constant" or is it knowable and small?

It's a function of the language you're writing an interpreter of and the language you're writing it in. "Constant" in that it doesn't depend on the programs you're going to run in the new language. i.e. for any given pair of languages there's a finite amount of disagreement between those two versions of the Solomonoff prior; but for any given number there are pairs of languages that disagree by more than that.

Is there a specific UTM for which we can always write a short compiler on any other UTM?

No. There's no law against having a gigabyte-long opcode for NAND, and using all the shorter opcodes for things-we-intuitively-think-of-as-complicated.