There is an old-school book that I have seen a few times in Siskiyou County up there that has a marginal mile by mile guide, you might be able to finde a copy at the book shop in Mount Shasta. Stanley and Holbeck guide will highlight the few notable rapids below iron gate. I would estimate 85-90% of the run from Iron Gate to Ishi Pishi is class II or below so a mile by mile guide might turn into a pretty boring read.
Happy Camp down is going to have the most action with quite a few class III's but still lots of flat between the action. Spring on the Klamath is fun and the toughest technical rapid (Dragon's tooth) becomes an easy class II at peak flow. California Creekin has a pretty good break down of the whole thing...
California Creeks - Klamath Iron Gate
California Creeks - Klamath Happy Camp
They have lots of class III rapids listed in the write ups and since your buddy is going in the spring, most everything turns into fun wave trains with moving water in between. Sounds like a fun trip, the Klamath is a beautiful and special place, hope that helps a little.