I sympathise with you,
All I can add is to be extremely careful as accidents can happen so easily and a damaged cone is something to be avoided.
As suggested an oversize screw could be worth considering but again take extreme care.
The newer screw heads that take hex drivers are far safer than a Phillips-head screw or the dreaded slot type. The hex fit snugly and are held in place so accidents are unlikely.
A bolt that just fits in the hole could work as adding little angle might be enough to break the seal.