REST is great for queries only, especially the BAQ Service.
And I would be remiss to not to mention that REST is more secure than ODBC and doesn’t suffer from all of the other issues surrounding direct database access.
As a former Access developer, I understand the the ease of creating applications in it. We have a ton of Access databases here too. However, I’ve found that the effort of having to have to maintain the client at every workstation a pain - not to mention patching moderate security vulnerabilities. This sounds like a simple web-app. You wouldn’t have to maintain an Access client on every workstation, and you’d be able to get the information available on phones and tablets too.
Just a thought from a recovering Access addict.