if the vac mod is bad, replace it, they are cheap. shifting hard could be from a "shift kit" a previous owner installed. shifting late at mid-full throttle is related to the governor in the trans.
starting in any gear is from a seperate mechanical linkage for the ignition lockout connected to the steering column. check if its still there, they get removed for headers & engine installs.
no reverse could be from an internal problem where its losing reverse. or it could be low on fluid, or a linkage adjustment. check the fluid first on a level surface with the trans fully warmed up from a drive if possible, check in park engine running. add the correct fluid if needed.