Best time to grease the gearbox splines and the final drive splines is winter time -when you're not riding too often. Take the time to clean out all the old grease packed into the dark, lower reaches.
!300 miles would be very early for a spline lube. I wouldn't even look before 5K.
I've always used Honda Moly-60 on my Airheads. If that Honda grease will handle the abuse from an overloaded Gold Wing, it should be fine for my Airheads.
I'd suggest checking the final drive splines and using that observation as a sorta gauge for the trans splines. Most folks tend to over do the grease application. If you see considerable squeeze out, cut back on the grease, especially on the trans splines as grease sling out can contaminate the clutch plate.
Like the old Brylcreem ads say, "A little dab'l do you."