Nicole-not completely sure why your using 1/2 and 7/8 sockets on a 3/8 square shaft. I must be misunderstanding something... Please forgive me as I dont want to sound condescending .Anyways, When you say "star socket" do you mean 12 point, 6 point, or 8 point? An 8 point socket is made to fit on a square nut (four sides). Like Dale says cant you just put a 3/8"drive,3/8" (or1/2") ,8point socket on ,say, a 3/8" drive speeder?.
https://www.ebay.com/itm/Craftsman-3-8-or-1-2-SAE-Star-8pt-Socket-Any-Size-STD-8-pt-Point/381798162251?hash=item58e4f19f4b:m:m7CeHUJ01Mfxp32wIAS1hgA:sc:USPSFirstClass!44147!US!-1
https://www.ebay.com/itm/Husky-CB85-3-8-Drive-Speed-Wrench-16-Long-Speeder-Socket-Wrench-USA/282564609499?hash=item41ca29c5db:g:byUAAOSwuq9ZYmc1
