The steel rod have been machined with multiple holes from the other side that connect to this (final) hole. Remaking everything from scratch will be much work, so I really need to get the bit out..
Like it or not MORE work, yet to get it out and then.. the rod is buggered as well?
You don't HAVE any of the more reliable means that do not also near-as-dammit ASSURE you will f**k-up the rod in the effort ANYWAY. Don't HAVE the experience, dexterity, machine-tools, nor tooling to improve chances of success.
Or it would have been OUT, already, drills being dead-easy compared to bustid TAPS!
QED
Spark erosion / EDM, specifically - which one usually
hires done.
Can't get that done? Costs too much? Make a new rod and be more CAREFUL.
If you were not already aware of it, "start over" - small parts more than massive castings, of course - is the preferred professional "cheat", if only because we have the most accurate sense of what it will cost in material and TIME, can plan accordingly and "JFDI" to plan.
Shit happens.
Life is always too short and deadlines for delivery always too close to roll-dice on praying, hoping, wishing, whining, masturbating, or other general fucking about at solutions we
cannot implement even if we were willing.