Personally I'd go for the H1 engine. Compared to GTR stuff, H1 engine parts are dead easy to find- pistons can be readily obtained from Wiseco and Wössner for example, conrod kits are also available. As for tuning, both Jennings and Murphy are dated and more recent and up to date tuning info isn't available for the GTR, partly because cylinders are very scarce and nobody will sacifice a set easily. However, H1s are still being tuned by enthusiasts using up to date info. Proper racing pistons aren't available for the GTR and as far as I know never were.
If you want to go the 350 route, use a Kawasaki Avenger engine. Although there is little up to date tuning info for A7s, parts are much easier to find. Also, I believe the A7 offers more scope for tuning. The only advantages the GTR has are its 6-speed gearbox and dry clutch- though a 6-speed gearbox is avaliable for the A1-R in England.