A 3/16" hole through 1 1/4" of metal is going to be difficult, it is 6.666:1 ratio, only a solid carbide boring bar could manage that, and an undersize hole would have to be drilled first. If you have a 4 jaw independent chuck and can dial in the od to 0.0005" and parallel and the work allows it, then drilling from both ends seems a better way. I would use a solid carbide drill from APT, that type are stiffer and drill to size without reaming, but care would have to be taken to avoid clogging the flutes with swarf.
Proper deep hole boring rotates the drill and the work in opposite directions and really deep holes have very special drills which are supplied with cutting oil at 1000psi or more.
Edited By old mart on 20/12/2020 17:31:02
Edited By old mart on 20/12/2020 17:56:41