I believe that the Inboard is the type of accelerator that requires you to
remove the 8088 from its original socket–although you should check with
Intel to be absolutely sure. In any case, accelerator boards which work
this way are NOT normally compatible with the Bridge. The only 386 boards
I have ever heard of which are compatible with the Bridge are the Elevator
and the Sota boards. I forgot who makes the Elevator, but it's hard to
find and is–or was–ridiculously expensive.
I know almost nothing about the Sota, but others here are using it.