Any machinists/engineers on here? Snapped a plug :(

Hi guys, wonder if anyone is able to help me. Recently finished doing a gilera runner 300 conversion. Bike cut out the other day due to the spark plug rattling loose. Unfortunately my HT cap for some reason it seats EXTREMELY tight on the top of the plug. Anyway upon removing the HT cap the loose plug seemed to "jump" a few threads resulting in the plug not being able to be tightened or loosened. In the end I got p***ed off and out of shear frustration ended up using all of my might just trying to crank the plug out (stupid I know), this resulted in the plug snapping below the nut. I turned the engine over to blow out the remaining middle part of the plug so now I am left with the hollow threaded metal jacket stuck in my head. I bought a set of EZ-out's (LH thread bolt extractors) however when trying to remove the threaded portion this way it doesn't want to budge and it feels like I'm going to snap the extractor.

Any advice? I'm loosing too much sleep over this bike and would love to have it back on the road as soon as possible however I cannot remove the threaded portion with and don't see any other viable options. Other than send the head off for repair.

If there is any machinists/engineers on hear that are willing to remove this portion of plug and chase/tap/helicoil the spark plug thread I am willing to pay. I am located in Surrey if anyone is local and fancies the job!!!

Thanks guys!!