There is some discussion of the Russian 6H13C's here. I have a pair or the 70's Svetlanas. Not as enthusiastic about them as you are. The bass is very good as you point out but I find the treble to be gritty for lack of a better word. Not my cup of tea. If you are up for tube rolling, try the RCA 6AS7. You can find them, with some persistence and patience, below $15 on epay. Actually, I found that they were easy to find on the cheap last summer. Looking lately, not as easy.
If you can find a 5998 for a fair price, you might even like those better still. They may trade some bass impact for control with improvement everywhere else. A bit higher gain as well (or less loss as I think Doc B. pointed out). Not cheap, commonly going upwards of $100 and beyond lately, when you can find them. Really nice sounding tube but as always, YMMV.