I think you are right to be concerned about range of the remote. I have a V3000. The motor control box with remote receiver is inside a closet with sheetrock walls and particle board doors; all insulated. The remote works fine in most areas of the shop, but when I am at the far side of the shop, which is about 60 feet away line of sight, but around a corner so there is another framed wall in the direct path, the remote is iffy, especially if my body is also in the way. So your plan of moving the control box, or at least the receiver, into the main area is probably a good idea.
And you are correct that you should not run portable cordage through a wall or ceiling or as part of a permanent installation. You can run romex in the wall/ceiling, or conduit with individual conductors; either way you'll need a box at each end.
Splicing the low voltage wire to extend it is fine.