Before FJ40Jim schooled me above on OME lift spring design "flaws," I noticed your rig has longer than stock shackles. Looks like about 2 inches longer which, if a good guess, would make your lift 2.5" spring plus 1" shackle (half the shackle length since the spring eye is fixed).
The extended shackles have pushed the shackle springeye & axle in an arc down and toward the xfer case. Obviously, the lift springs moved the axle downward which, alone, should extend the driveshaft length required unless what FJ40Jim said means that OME locates the centerpin hole foward (iow, near stock distance from the springeye despite 2.5" lift springs being longer than stock by necessity of the lift involved) to keep the axle near the stock distance from the xfer case so generic customers can run their stock-length driveshafts or simply have the axle/tire biased foward to allow for no rear tire to fender strikes with the greater-than-stock movement rearward inherent with longer lift springs under compression. Generic customers probably don't take to fender trimming. Perhaps I'm over thinking the OME part of this. No reflection on Jim.
Another clue that the springs are too short for the shackles is the vertical position of the shackles. The shackles should angle towards the rear some like the stock shackle position which gives a good ride, relatively speaking. With vertically positioned shackles atttached to positively arched springs, the rear spring eye must first struggle back before it can more easily arc upward.
Only springs made longer for the extended shackles with a centerpin hole location placing the axle in the stock, unbiased front or rear, location would bring the axle back to what you seem to expect from lift springs (me too). Custom springs are probably your only SUA option where the springmaker makes the rear springs with the lift amount and shackle length in mind. Not to mention pinion angle, axle location, vehicle weight, and usage (rockcrawling

). You could then trim the fenders around the "properly" located tire to allow for axle movement rearward under compression.
I still don't know for sure if the 37s would work in SUA configuration with a 3.5" to 4" spring/shackle lift and fender trimming; I just know that the spring and shackle combo you have are not compatible with where you (and I) expect the axle/tire to end up under the lift. HTH.