I play crossharp myself. If you are talking a bluesy
crossharp, it's not that hard to record if you have the right mic and amp gear, actually. The amount of dirt you gear throws in isn't all that important
.
Start with
an Astatic JT30 handheld, if you can get you paws on on one. If you're not lucky enough to have a vintage capsule like that (and many of us aren't), any kind of handheld bullet will do, even a Shure DX50 Green Bullet, though those are a bit on the big and heavy end of the bullet design, and are a bit on the "modern"-sounding side. They'll still work fine, though. If you can't get your hands around a bullet, you can even use something like a Shure 58 or any other ball mic. The key is you want it handheld so you can get the harp right up to it and so that the player can do his proximity/cupping tricks. A stand-mounted mic at even a couple of inches just won't cut it the same way.
Run that mic into a small, gritty amp; anything from a Pignose on up, frankly, preferbly with a tube or two that can be easily overdriven. Close mic that with Sen421 or a 57 (whichever sounds better for your particular chain) and run it pretty clean into your recorder. You shouldn't need much comp as the cupped mic and overdriven amp combo should be delivering a fairly compressed package as it is. Leave EQ alone unless you need to cut something irritating from the amp itself.
If you're talking more jazz-pop chromatic harp stuff a la Little Stevie, then I'd agree with Harvey's placement front and above the harp; keep it above the breath and the spit LOS of the player
and get a warmer, cleaner sound. You can comp that as necessary (but not too much) and run straight to preamp.
G.