It's tricky. There aren't many boats going out during the week, and oil rigs trips don't even happen every weekend. Catalina/oil rigs trips go out of Long Beach/San Pedro while northern Channel Islands trips go out of Ventura, at least an hour's drive north. So trying to do both in the same week leaves you with few options, and it looks like what you've come up with (northern islands on Saturday, oil rigs Sunday) might be the best way to squeeze it all in, if those criteria are really important to you. But I would suggest you consider other dive sites on Catalina (i.e. a day dive boat, not the ferry) instead of the northern Channel Islands, at least for this trip. There is such a huge and varied array of sites all over Catalina. There's more difference among dive sites on any given island than there are between different islands on the whole. You don't really get to pick the sites you go to; the captains choose based on conditions. You could luck out and get something memorable and incredible, or you could get something that leaves you thinking "is that all?", no matter which island you choose. So maybe it's worth sticking around the Long Beach/San Pedro area and diving out of there. Another area you might consider, accessible by boat from that general vicinity, is Palos Verdes.
I see you already have Eco Dive Center's boat schedule, since they're chartering your oil rigs trip. Big Blue has a Catalina trip on the 17th:
Bigbluediveboat
Channel Islands Dive Adventures is doing a Farnsworth trip to the backside of Catalina on the 17th, which is also a relatively rare opportunity; it's an advanced deep dive, like the rigs, but it's probably my favorite:
Dive Calendar for Southern California - Channel Islands Dive Adventures
You can also check back with Ocean Safari in a bit (they haven't posted their July schedule yet):
Ocean Safari Scuba | Upcoming Scuba Dive Trips to the Channel Islands and Beyond
If you're still looking as the date gets closer, hit me up and I might know of something else.
You should also give some thought to the logistics of getting your tanks filled between dives. How many are you bringing? Boats usually expect you to show up with a full tank; they'll fill it between dives but not after your last dive. Sometimes you can sweet-talk them into giving you another fill at the end (ask as soon as you get back on the boat after your last dive, not when the boat is already heading back, and tip well), but you should have a backup plan in case they won't. A handful of boats actually don't fill tanks, and those that do mostly only do air, not nitrox. (The Magician used to have a nitrox system but it's been broken for about a year and I've kind of lost hope it's ever going to be fixed.) There are lots of dive shops in the area, but few are still open when the boat gets back at the end of the day. Pacific Wilderness is probably your closest option in San Pedro; I believe they close at 6 on Saturdays, which is cutting it really close.