I would have to say keep the sip 346 item, especially if the other secondary stat is mastery. As h priests spi is our bread and butter, more so than the other healing classes IMO, due to holy concentration. Now on my healadin, I'll sport a couple 359s and forge spi on them, but only a couple.
It's not going to kill you to have a few pieces without Spirit, especially if they are a pretty big upgrade Intellect-wise, and especially considering the reforging option. Don't overdo it, don't roll against your mages and warlocks on non-spirit gear (in most cases), but don't immediately write off an item simply because it doesn't have Spirit.
For the pieces you listed, I wouldn't waste the gold on the BoE chest when you can get the tier one from VP. The Earthen Ring rep gloves are pretty nice (haste/mastery if I recall correctly), I would go ahead and use them once you get the rep.
Yeah the spellpower and mana gains from upgrading are nice, just don't go overboard. Reforging for Spirit on those 359s helps - just understand that gear is basically a placeholder until something better comes along. One or two pieces, depending on slots, is probably okay. You are giving up a lot of mp5 just by not wearing a piece that naturally has Spirit on it.
I would stick with spirit stuff, imo. Generally you should have enough throughput already that you should be worried more about mana longevity. The first example, the chests, you are losing spirit to gain mastery (and a bit of spellpower), which won't help you as much as the spirit will. The Flamebloom gloves are nice, but since you are considering a BoE epic (Grips of the Failed Immortal) you can get Woundsplicer Handwraps which is even better.