Forum Discussion
Export and Link Access Query to SharePoint Online
In a nutshell, your first scenario is exactly the way you need to go about this. Convoluted or not, you export your tables to SharePoint Lists, then link the accdb to those lists and, optionally delete the original tables. You COULD also just create a new accdb and link the lists to it, instead, but that probably isn't really worthwhile.
You might get some useful ideas from this AUG presentation. It's aimed at using Access as the Front End, but you could connect to those same SP lists from a PowerApps application and have a more versatile hybrid application. This AUG presentation introduces some of the concepts I personally think Access devs need to consider when adding PowerApps to their portfolio of tools. And I created a set of YouTube videos on managing larger data sets (exceeding the 2000 record delegation limit) in PowerApps).
All in all, I am convinced you are likely to find extending the reach of your robust Access relational database applications to the mobile environment a great strategy.