If the depth is what you are showing in your photo of the regulator, run a dremel cutting disc over each screw putting a slot on them and remove them with a screwdriver. Don't be afraid to go into the old regulator if need be.
Grinding down your cheapest 7mm socket to a tapered point would not be hard to do either. I would use an angle grinder myself with a sanding disc after fixing the socket on an extension and running it in the drill press.
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