Spud, not the best person to offer suggestions, but here goes.
Suggest you make sure you are in C.G. compliance.
Also a GPS and/or compass are good things to have. Allows you to leave site of land and get back as straight as possible.
There are several petro rigs within site of Packery, mostly SE or S-ish of the jetties there. About 2 miles out, I'd guess. Hard to miss.
There are other rigs within 10-12 miles of Packery, don't know of any rocks or wrecks fairly close.
I'd think there will be a chance at Spanish Mac, shark, kings, snapper, Red snapper will probably be small, (you might get into Mangroves at the rigs fishing close to the structure), maybe redfish, bonito, and other fish. You might hook Ling, tarpon, bluefish, Jack Crevelle, etc, etc.
Simplest way to fish if to use a carolina type rig, put a egg sinker on the line, swivel, leader then hook. Drop it down with a bait, live or dead, and see what bites. Vary the depth. Also drift a whole bait out with the current, possible hook up something that way.
If you get cut off, break out the single strand wire you bought, and use a leader of that.
If you want to troll, Russell Lures are simple and will catch fish, as will other diving baits. Make wide turns around the rigs.
You got chum, drop some of that over board at intervals, not too much is needed at one time, slick will hopefully bring up Blacktip sharks.
However, Shrimp season opened a few days back, so a lot of sharks will be behind the shallow dragging shrimpboats. If you see any dagging, come up behind the stern, hit neutral, drop a bait over and drift, might be some big Blacktips where the net is dragging. Be careful of the net, if you're in 20-30' or less of water, you can get hooked up on the net, and you'll get spooled.Never heard of a shrimper stopping 'cause someone foul hooked their net.
If it's not too rough try tying up to the rigs, but be careful trying it.
If you've not seen Packery, suggest you drive over the 361 bridge around noon time, slow down a bit and look over the channel, looking for the deep water, traffic, etc. Do it couple of times if needed.
Here's a page of coordinates that might help, based out of Port Aransas. spots http://www.fishingportaransas.com/htdocs/structures.htm
Remember the Federal rules for some fish are different than states rules.