I had a thought today.
With vertical dropouts couldn't you just physically shorten and lengthen the chain to get good tension?
You could use half links to get it just right even.
But my thought was you'd probably end up with a really weak chain after all that tinkering.
I dunno, just some crazy thoughts.

that's a lot harder to do than you'd think.

You've got to pop links out and then push them back in and it's a pain I know, that's why this isn't a feasible method. But it could work.

Google magic gear.

I've done half links, filing sideways vertical dropouts and filing flat axles, and trying different cogs and chainrings. You also have to factor in chain stretch.

I've experienced all this stuff.
Never filed my own dropouts or axles, but I've seen guys do it.
It always seemed like a lot of trouble, but they were in love with these frames, so I guess they couldn't just forget it and get a new one.

ive tried all those methods, suck it up and buy an unsightly chain tensioner, ugly but you will be glad you did. and... you wont lose any ride time or sleep!!!

eccentric hub

The chain's going to stretch any way. Why even bother.

Exactly.

Yes,and what do you do when the chain stretched,garbage.

Yeah, I'm doing it. It's been a year and not enough stretch to fret.

Eccentric BB, I love it. This allows you to use a disk brake at the rear.