Converting it to modern tools can definitely be done in a safely manner. I personally would start by running the new system in a separate network, just re-processing the requests that had been processed by the old system and checking it they came out with the same result. I would leave that on until it got to at least a year without any differences between the result of both systems. Only then would I start considering replacement.

I wouldn't trust such replacement on 95% of people I've worked with before. I definitely wouldn't trust someone with Elon's track record to manage it.