Redline MTL, Royal Purple Synchromax, and Amsoil Synchromesh are all good choices for the NSG370 (at least the LJ version, though I don't think anything has changed in the JK years).
That said, you just described every manual transmission in existence. Manual transmissions don't typically have pumps and operate by "splash lubrication". As a result, they don't warm up fast (and only really warm up by driving) and are generally tight and clunky until sufficiently warm. If you've just change the fluid, there's no need to change it again.