I’ve heard, anecdotally, that .40 to 9mm conversions can result in unreliable functioning. The 9mm recoil just doesn’t operate the heavier slide and/or recoil spring of the .40 as reliably.
A .40 to .357Sig should work well, and the magazines are compatible. Perhaps try that route?
With current ammo shortages, it sure would be nice to have the ability to shoot multiple calibers. I solved that problem by buying many different calibers...an expensive option, I admit... ironically, because .40 fell out of favor for a while, I was able to stock up on it at a very good price earlier this year. Even after the ammo shortages started, .40 was still in stock.
Now, everything is in short supply, and manufacturers will make the most popular calibers first, like 9mm, 5.56mm, etc. so the .40, and other less popular calibers will take a much long time to return to the shelves of suppliers.