I run dino 5w30 in the winter, but I have been thinking about synthetic. If I were to run synthetic in the engine is probably would be Royal Purple.
As for the tranny, we need to know which tranny. The AX-5 and AX-15 take 80w90 oil and the NV-3550 takes synchomesh I believe. I ran for the longest time dino 80w90 but last spring I put in Redline synthetic 80w90 and it made a big difference. Smoother shifts, easier on cold days, and made the tranny quieter. I have the AX-15 with 220,000 kms on it.
In the t-case, which take ATF, I put in Royal Purple synthetic.