The Cream-of-Tarter is an ingredient a friends in Colorado tipped me to and when I have it, I use it. If I'm out then I don't let it bother me too much.
Back in the latter '90s he suggested using Dawn dish soap and, at that time, it worked better than several other brands I tried. I question, however, if today's product is the same or not as I had some poor results a couple of years ago. Today, I usually round up my coin cleaning supplies at the local Dollar Tree, if they have it.
As for the toilet bowel cleaner, yes, it definitely can help! One thing I forgot to add the the list of supplies I use are some latex gloves. Also, it's handy to do the coin cleaning in a well ventilated area due to fumes from the cleaning solution (TB Cleaner), and I use gloves to help protect my hands and any small cuts or sores.
Prior to the general cleaning, tumbling, rinsing and drying I "pre-clean" all the different groups of coins. They should not be in the jar of Toilet Bowel Cleaner for very long. I put in about 1 cup or so, cover with liquid, put on the lid and agitate and shake it up well. I want ALL SURFACES covered/treated, and then it might sit for 5-15 minutes. I then shake it up well, pour all the contents into the plastic butter/margarine tub, then salvage as much of the now used liquid as possible by pouring it back into the peanut butter jar (the plastic tub lets you pinch it closed to help retain coins), and then I aggressively rinse all the coins.
"Aggressively?" Yes, I run HOT water on them in the plastic tub and (wearing gloves, usually) I keep mixing them all around to ensure that they get well rinsed to remove the TB cleaner. I then pour them out on a terry cloth towel to dry while the tumbler finishes with the current batch. Remember, I said I only tumble them for 30-60 minutes.
As soon as the tumbled coins are out for rinsing I put in the just treated coins and tumble them. While they tumble i can finish the rinsing and separating of the aquarium gravel and coins, rinse the coins in hot water, then spread them out on the towel to dry. Untreated, I often end up with a lot of ugly-looking dimes and quarters, as well as dark, ugly pennies. After treating and tumbling, I will only have a few that are not presentable The fertilizers use din lawns as well as the natural chemicals in the dirt, sand, and wood-chips (especially old, deep gunge) can leave coins quite altered.
Monte