Doing this with the other hole empty is hurting your cause. Using another fully lubricated bolt in good condition to relieve preload sometimes makes this situation go easy and is always helpful. You mount an SPD cleat by alternating back and fourth until both bolts are torqued since preload on one relieves it from the other, so you need to employ the same principle in reverse here. Grease the shoulder and tighten it to the brink of breaking something.
The bolt head doesn't look so destroyed that a good 3mm wrench in good condition will get nothing on it. If that is the spot you're in, using a dremel cut-off wheel to make flathead screwdriver flats usually works well on SPD bolts. And then if that doesn't work, just go the rest of the way down with the mini end mill dremel bits to obliterate the center of the bolt head.
Some shoes are put together in a way where the tongue and insole can be made sufficiently out of the way to use the plate as leverage from the inside. In other words, if the plate is resting on the sole as opposed to being inset, you may be able to twist it with the other bolt out. If you were up against corrosion as opposed to preload, that approach could also work.