For toothpaste, I give you several options to ponder:
One, since I just got back from Target to confirm, the standard travel sizes of Crest and Colgate are 0.79-0.85 oz and sell for under a buck. However, there are some Aquafresh travel sizes in 1.3 oz for under 99 cents as well. All are legal.
Two, I switched over to the Crest or Colgate liquid gel toothpaste a while back, simply because they lay flat in my shower kit. Unfortunately, the smallest size of those is 4.6 oz, so to big by a bit to not get noticed. However, you should be able to drain that kind of toothpaste into a smaller bottle to take with you. I do this with shampoo and hair gel.
By the way, if you don't lable your bottles, make sure you pick bottles of different size or liquids of different colors. Brushing your teeth with hair gel would really suck.
Three, put the toothpaste inside your bag and hope it isn't spotted.
Four, put the toothpaste in your pocket. I haven't heard of TSA agents asking people what is in their pockets or anything, but I don't recommend walking through with an 8-oz tube in your shorts, although that would be funny. "Is that an economy-sized tube of Crest Whitening in your pocket or are you just glad to see me?"
Five, check it. It's funny when Comrade Hawley seems to still recommend checking all bags "so you can breeze through security". Yeah, I'll make you work a little bit at the checkpoint to save me the extra 15 minutes on departure and 15-45 minutes on arrival waiting on a bag.