If you show the staff both BP when entering the lounge, I'd reckon they will dutifully direct you to the TPR or at a minimum the F Lounge (if leaving from T3). Personally, while the TPR is a fine lounge (not earth shatteringly awesome, but very good), it is still not a place I would want to spend an extensive period like 9hrs. Post arrival you could grab a quick bite or such if desired and then maybe head into town to stretch your legs and enjoy some local food (the MRT / subway is very easy to ride into town and back) and then I'd show up maximum ~3-4hrs prior to the SFO flight to freshen up (shower, etc.) and have a snack or drink or both - depending if / how much you indulged in Singapore local fare or not.
YMMV.