Do you have an photo of the battery?
I use J-Type as well and have not experince that issue.
You should "Not" have to remove the motor plate as the fuse case should tuck into the middle hole in the motor plate.
Your battery has the upper channel to tuck into, so you only have just the connector and wires to deal with. Allot of people remove the fuse case but I guess that won't solve the battery issue.
I'm guessing your battery is wired to the long end of the battery? It should be wired at the short end of the J.
I have changed my battery to deans plugs to lesson the space taken up by the small tamiya connector.
Hope this answers some of your questions.
cheers