You will be fine utilizing in your transmission a known brand SAE 80W/90 Hypoid gear oil that carries the API (American Petroleum Institute) rating of GL-5. This is what keeps the gearboxes happy in my '81 and '83 R65s.
As to using a synthetic gear oil, your tranny oil seals may begin to leak with the thinner and slicker lubricant. Some Airhead riders have experienced this with the older OEM seals. The leaks disappear after returning to a dino oil. YMMV.
Your shifting scenario is not uncommon with the Airhead gearbox and really may not indicate a lubricant nor mechanical problem. Correctly timing the down shift, full shift lever throw, plus matching gearbox shaft speeds, gear engagement dogs, engine and road speeds, needs a nicely trained left toe.
Tis a beautiful thing when it all comes together.