Odd, odd, very odd for the guide to book as such. Many guides do flip-flop up here between the saltwater and the river and perhaps that is his plan. The Kasilof River, the river on which I guide, is open for guided fishing on Monday (the regs you're discussing are correct), but we lost our Sundays beginning this year.
Typically, our success rates on the Kasilof are considerably better than those on the Kenai (the site you mentioned has good stats on harvest rates) ... but with a smaller fish typically the result. Keep in mind that the Kenai is NOT an action fishery ... it is limited action usually with very nice fish in the 35-40 pound bracket and the outside chance of hooking a true monster. July kings in the Kasilof average 25-30 lbs. with our big fish in the 55-60 pound bracket. Perhaps your guide plans on bringing you here one day ... although most of the guides on the river in July are regular guides that only fish the Kasilof. July 8-12 is a tad early for the best fishing on either river, but there will some fish available.
You won't be able to take your guide's boat ... the regulations read that fishing is prohibited from any craft registered with Parks (the boat should have a round sticker and a three digit number assigned to it) ... so even if the guide is not present, you still can't fish from the boat on the Sunday. Monday on the other hand, is closed to all fishing from motorized boats, and all guide boats (drift or power).
King fishing from the bank is basically hopeless unless you have some very privilaged info ... and you're going to be early for the sockeye. Which leaves you with just a couple of bank options: Homer Spit Lagoon for some late first-run/ early second-run kings, and the smaller streams (Anchor, Ninilchik, Deep Creek) for dollies and perhaps some humpies (there may be some of these in the Kenai as well, but again, likely a little early). You can find a little info on these areas in our "fishing on your own" area located in the Alaska portion of our site.
If what you are telling us is correct, that someone booked you for four days on the Kenai including a Sunday and Monday, then I'd be very leery ... if your friend didn't pass all the info along, then perhaps everything is just fine and you're getting too worried