the very definition of "interesting" or "cool", as opposed to "good".
you're right, harmonica is a legit exception i suppose, where it's treated more like electric guitar and the amp's coloration is actually a key part of the tone. i think most serious harp guys use high-impedance mics that are already 1/4" unbalanced, though.
Yep. I have a vintage AIWA mic (yes, the Japanese company) that has a crystal element and i have it hardwired with a 1/4" unbal connection for an amp. This is very common for harp mics. Old Astatics and other Ham radio, aviation, and paging system mics are used for harp, and they're mostly Hi-Z or they work just fine with Hi-Z inputs on amps.
My mic sounds great.
Getting back on topic, I would see no issue with a Jensen or other impedance transformer being used "backwards" from the normal convention. It's "backwards" only because it'd be counter to the normal DI flow. But it's a transformer; it works either direction. The iron and wire don't care which way the electrons and magnetic currents flow. They work both ways.*
The only issue might be jack switching or something like that, but if you've got cables in both gozintas or gozoutas, then I think you're probably OK on that score, too. Otherwise, you might have to rework some jack switching scheme.
I would suppose that any normal DI like a Countryman, Radial, Rolls, etc. would work just fine as long as it's passive and uses a conventional transformer.
*Unless you buy a Hi-Fi unidirectional cable for $1000, then it matters.

Except for that pesky detail about music signals being alternating current.