Alum works just fine and doesn't take too long if you use it properly.
Make a saturated solution or see if your local water treatment plant will give you a pint. Put it in a plastic bottle.
You will need to adjust your dose based on how turbid the water is. More turbidity will need a little more alum. Too much is counterproductive. You really need to get the dose right. It helps if you have some soda ash to adjust the pH to the ideal range for settling. Keep in mind the source water may already be alkaline and need no adjustment. Not only will too much alum keep the water from settling, it can add a metallic flavor.
A little practice will help you get the dose right. For a five-gallon bucket, I typically go with about a half cap full from a liter tonic water bottle to start and adjust as days go by or source water quality changes. After you dose the liquid alum, get a paddle and really slosh it around violently, but just for a half minute. This gets the alum distributed in the water and in contact with the sediment to form floc. THEN use the paddle to gently swirl the water. This allows the floc to continue to grow and not get broken apart. For a row of buckets, I dose, rapid mix each one, then get the swirl going. I go back a couple times to keep the gentle swirl going, and then walk away. The primary settling happens pretty fast. You can decant fairly clear water in a half hour. I like to wait an hour or more before filtering to drink, but for dishes, you can get clear water ALMOST as fast with alum as with the PACl, but the PACl will certainly work.
I think you still need to be mindful of the dose. You may not need to worry as much about pH. I just use alum as it's really cheap and easily available. Oh. And it does work just fine for my needs. I hope you find something that works for you.
My name isn't actually Will.
I live in the Willamette Valley about a half mile from the Willamette River.