Has anyone found a go-around solution for continuing to use Fujitsu Scan Snap S510M with Catalina?

It turns out that the paid, non-subscription, 64-bit VueScan supports the S510M, and ix1500 models without any Fujitsu software or drivers installed. Fujitsu has Catalina support for the ix1500 with caveats regarding earlier software.

You don't tell us much about what your problem is. I assume that you have a Fujitsu scanner which can no longer scan. What happened that caused this to occur? Was it an upgrade to Catalina? Something else? If so, that would suggest that your Fujitsu scanner software is an older 32 bit app. The first thing to do is go to the Fujitsu web site, under Support, and see if there is an upgraded software download available (64 bit). If not, you can do a free trial of the VuScan app. If it works, the purchase price is reasonable and it offers a lot more features than most vendor provided apps. Last, you should be able to scan using Apple's Image Capture app, but it doesn't have all the features and is a basic scanner.

Otherwise, you need to provide us with some specific information as to what your problem is.