Bolts are illegal within the GCNP. Basejumping is also illegal within the GCNP as found out by McNamara on the TOmmy Caldwell trip. He was banned from the Park for 5 years and given a hefty fine. If the Park was lucky enough to catch you in the act, the TL and trip might get a free helicopter ride out.
Probably shouldn't be climbing overhead if you can't build a traditional anchor. The Canyoneers have become quite proficient in traditional anchors. One technique they use is drystacking a pile of rocks with webbing around it:0 Pretty hard to do for the first time if you've been rapping off of bolts.
If you can con your trip into camping at Badger, there's some multi pitch cracks that go way high. Bring OW pro. Every once in awhile you will hit a solo bat that will send the tinglers up your back hairs
I've found, unless your trip is all about climbing, you will have a hard time encouraging the group to wait for someone climbing except bouldering at stops or in camp.
Checkout Grand Canyoneering by Todd Martin, best guidebook I've seen!