Unfortunately, I have not spent time thinking about it.
Here is what pops to mind.

We can offer the JPA 2.1 level support (AttributeConverter) which essentially remains a simple object to object bidirectional conversion.
In this case the converted type should go to the regular dialect type conversion logic? (say a custom type is converted into a URL)

We can also offer something intermediary by exposing Tuple + metadata. Compared to the JPA 2 converter, you can write several columns for one given property. Say a Amount can be stored in two columns, price and currency.

The last I can think of is exposing dialect specific APIs (say the mongo command to execute). but that's 1. specific to the nosql targeted and 2. not sure we can do something clean enough.

I would focus on 1 then 2 initially.