First of all, pay attention to copper balance. Uneven amounts on layer pairs (top/bottom, mid top/mid bottom, etc.) relieve internal stress unevenly, and that's where the warpage comes from.
Or it's a manufacturing error, in which case just as well to send it back and demand fab to spec -- assuming you have controlled for the above case, your board spec requires it, and you paid for the service to follow that spec, of course. (Proto services give no regard for your specs: the specs are listed in their spec sheet. If their specs don't meet yours, get a custom run, or go somewhere with tighter proto specs.)
As for where you are now, if you're not willing to scrap the parts, yeah, something that flexes the board is about the most you can hope for. Differential cooling may help (i.e. heating things up and quenching stretched areas), though I don't know how well this works with a laminate (it's a traditional sheetmetal method). I do find, when tinning copper clad for protos (i.e., not etched and soldermasked PCBs, just plain 2-sided copper clad), it ends up warped, presumably due to the shrinkage of freezing solder as I tin the surface a bit at a time, and probably some help from the copper and laminate shrinking differentially as I go. This usually cancels out once I've tinned both sides, or just flex it a bit to work out the stress. (Note: this must be done before placing components; flexing a board with chip components on it is not a great idea!)
Oven time won't help: it was manufactured in a heated press, between flat platens. You can try preloading a bend to cancel it out, but if it's a warp rather than bow or twist, you'll have a hard time with that (you have to stretch everything that's
not sticking out).
Time and temp isn't a bad idea; laminate creeps a bit over time (accelerated by heat), and takes a modest set on deformation. So if just flexing it doesn't help, heat might. It's just, getting the strain everywhere but the affected area, isn't going to be easy, I suspect.
And, to clarify a bit on topology: zero Gaussian curvature is like any way you can bend a sheet of paper (without like, getting it wet or something). These are easy: simplly bend and twist, you can just flex these out, no problem. It's when it's nonzero that it's a problem. For domed curvature, it's that the middle is larger than the surroundings, so domes out from it; either the middle has to be shrunk, or the surround has to be stretched to match. You can squish down the dome to undo most of that, but you can't do it any further than pressing it down flat -- there's no "flatter than flat" you can force the material into, and in that flat shape, the material will still hold some stress, and spring back from that position. For saddle-shaped curvature, it's that the middle is smaller, and needs to be stretched out. (This can be done by doming it, at least in part.) In either case, it has to be stretched evenly, lest you just make things worse!
You can also consider adding brackets or frame rails or a chassis or whatever, to enforce a more rigid shape on the board. This is probably a non-starter for assembly (good luck doing pick-and-place and reflow soldering like that..?), but good practice for final assembly, for obvious reasons.
Tim