Spray it with some penetrating release fluid and leave for a few hours or overnight.
Then perhaps tap a screwdriver bit into its centre, something like a hex or slotted bit.
Or reverse threaded extractor bit as you say - however I've had a bad experience with these extractors snapping off in the hole, perhaps mine were cheap.
The key is a nice tight fit, without the bit starting to spin in the hole.
If that fails even try a Left hand threaded drill bit (obviously drill running backwards) into the centre of the screw. Hopefully the leverage and backward pressure from the drill bit will release the screw from its thread.
Would be best doing this on a workbench, with the Caliper in a clamp, so you can get decent leverage/weight behind it, plus some precision. Best of luck!