Actually, nuking might work.
Am I correct to assume, that you have about 5000 feet of water. Then about 13000 ft of bedrock before you hit the oil and gas?
A small nuke detonated half way down might just solidify the rock around the hole.
It could be a very small device, enough to produce the heat needed.
Oh one last comment... PHU*K the environmentalists....
If we can get a nuke down the well then we can get cement down the well and theres no need for the nuke.
I don’t know about 13,000 feet of bedrock, but the subfloor geology is probably well know from all of the seismological sounding that found the oil in the first place. but even 13,000 feet of sand is sufficient. The water pressure at 5000’ is about 2500 psi and should provide a dampening effect on top of all that.