I must have missed that in the first read. Yes, do not do this.
If anything survives the hype cycle for microservices, I hope it’s this: if your company isn’t surviving more than a couple of technology cycles, especially when they seem to be getting faster, then what are you doing this for?
Stop trying to replace one system with another one. Yours will be old and busted someday too. And certainly don’t let one system be the gateway to the other. Put them both behind a thin layer that handles only a couple of concerns (say, auth, making sure all requests have a correlation ID, perf statistics, maybe pick 2).
What we are both suggesting, I have still always called the strangler pattern. It just has three actors instead of two.