Grocery store alum is fine.
There is no cheaper, more effective way than alum if you have 30-40 minutes to let it settle. It should be the first thing you do as you make camp is to set up your settling pots/buckets so later in the evening and the next morning, you can process it. For overnight, you may be able to skip the alum (do one test bucket the first night). But if you want clear water in 30-40 minutes, use the alum.
Use about 1 gram per 20 liters / 5 gallons. An easy way to measure it is to have a "pre-mix" bottle with an ounce of alum ("shaken, not stirred") in a liter of water. Then a 1/30 of the bottle (1-2 capfuls) will be one gram.
Use more pots/buckets so you have no temptation to drain off the bottom 1/4 of the volume. You'll quickly find that bumping or kicking a pot spoils the results. You'll also develop a very smooth technique for decanting off the clear water. taller buckets make this easier to do without disturbing the sediments on the bottom.
You're exactly right that you want to skim the scum. Do that early and let the sediment resettle. Or skim the scum VERY gentle. Some river water has very little scum - no floaters, all sinkers. You'll find out the first day.
5-gallon buckets are wonderous things - cheap, fast, large capacity. But you're in a pack raft? So maybe you don't have a lot of room?
Very compact, light, and free alternative to 5-gallon buckets:
Go dumpster diving at the recycling center. Score LOTS of 1-gallon milk jugs. Use sturdy scissors to cut off the top half (never use a razor if you can possibly use scissors and you'll reduce trips to the ER). Play with the height - 3" high nest very well and make very cheap and light serving bowls/plates. 5-6" high hold more water each (duh) but don't nest as well. But you'd a lot of such 1/2 gallon "bowls" to equal each 5-gallon bucket.
A micro-civil-engineering project ("the kitchen sink"). The ultimate compact water container is a hole in the sand lined with a tarp (or, in a pinch, a WP parka, but its going to get muddy). Ferry water to the "sink", add alum, stir, and decant off the clear water 30 minutes later. 2' x 2' x 1' = 30 gallons. Dig less soil by piling the spoils up as a lip for more height. Avoid digging through tree roots - they go a LONG way in the desert.
A mini-mechanical-engineering project: I've been know to bring ten 24" x 24" plywood panels, secured together with 2" nylon webbing, and then lining it with a tarp. A 6-foot-diameter hot tub holds 8-10 naked college students and each human is 15-20 gallons of water you DON'T have to schlep or heat up. Then there's heating the water, but that's a whole other thread.
But don't short yourself on water storage. If you aren't packing away enough treated water the night before, stop again mid day and let another batch settle during lunch. It is appropriate, IMO, on a desert trip, to frequently ask companions when they last peed. If the answer is more than 2 hours ago, they HAVE to drink a full liter then and there with another one to be consumed, perhaps more slowly in the next hour or two. Women usually do less stupid stuff than men do, but some will minimize fluid intake to avoid frequent potty breaks. That's not good.
The work of pumping through filters really sucks in a hot environment (we did a GCNP private raft trip a few years ago). I'd do some UV and iodine or chlorine AFTER the flocculation in a clean container without the sediment.
But if you are filtering, I think you'll be getting water so clear that you needn't bother with the pre-filter.
Edited to add: label the pre-mix bottle. Wrap it in red tape or something. You don't want someone drinking all the alum solution. While at the recycling center, I'll offer grab various HPDE (my favorite plastic) bottles and run them through the dishwasher at home. Something like a hydrogen peroxide bottle is totally food-grade, has a secure lid, and is pretty sturdy (less like to get punctured), but no one will mistake it fro a water bottle.