You gearbox will be happy with an EP 80 /90 gear oil with a GL4 spec. GL5 is too slippery for our older type gearboxes and it can seem like the synchromesh is on its way out if you use it.
Editor of the VVOC Magazine ReVival
"When you have a Firenza like mine, who needs any Minis?" copyright David Maxwell 1979.
Yes, 80/90 is fine, and I've used it in my HA. Topping up is a bit of a b*****r though, as the filler hole is high and close to the tunnel, unless you have a pressured supply, or an oil bottle you can squeeze, with a flexy spout! Gets a bit messy if you are not careful, and drips down your arms!!
I suppose you could, and would certainly be an easy way to get the oil in, but the filler plug is still on the side of the housing. The instruction is that you remove the plug, fill with oil through the hole until oil runs out, thereby ensuring it is at the right level, and then screw in the plug quickly. Could be done the way you suggest, but would require another pair of hands.