SAAMI spec for large rifle primers is 0.2105"-0.2130". (To see all SAAMI primer size and primer pocket size information, since some handgun cartridges use rifle primers now, you can just download
the SAAMI Pistol and Revolver standard and in the Acrobat Reader page counter at the top, put in page 35 and hit Enter. This takes you to the document page number 26 (the document doesn't give its index page numbers, but the PDF format does), which is where the primer and pocket sizes are.)
I grabbed a fist full of my large primer pickup tubes and found all the newer ones would all pass a 0.2190" pin gauge, and one old one would pass the 0.2180" pin gauge. I also had one large primer feed tube off my 550 and it just barely passes a 0.2150" pin gauge. My pin gauge set is a -0.0002" set, so that tube is between 0.2148-02150" ID. Likewise, you can subtract two tenths of a thousandth from the 0.2180 and 0.2190 numbers I gave to be closer to the limits of precision of the measurement. The point is, even a maximum size 0.2130" diameter primer would fit into all these tubes without an issue, as long as it isn't oval to the tune of 0.005" or more on one axis. That's an awful lot of out-of-round for those little guys, though.
Old CCI primers had quite a reputation for being hard to seat. I still have some from the 1980's that my Square Deal and 550 presses won't seat fully, but I never had an issue with them failing to fit the tubes. Instead, they tended to have burrs from the height trimming process. In the early 1990's ('92?) CCI revamped their primer making process and got rid of the burrs, so the modern ones are OK in the Dillon. If your old ones are actually more than 25 years old (date of manufacture, not date of purchase; they could have sat in stock at the store for some years if you purchased them a little after '92. In that case they would be hard to seat even if they weren't oval, and I would relegate them to seating with a hand tool, instead, which will still work.
The failure to fit the tubes, though, that's funny. I don't know how much mileage you have on your Dillon yet, but the tubes need occasional cleaning to get primer dust out to prevent in-tube ignition. You just get some adequately large cotton swabs and wet them with denatured alcohol and push a couple or three of them through the tube with the plastic primer follower rod, then let the tubes dry. Since you want to do that every now and again anyway, and since you are having feed trouble, something you can try is mixing maybe a teaspoon of powdered graphite in an ounce of the alcohol and stirring it up well with the last swab you run through the tube, so it leaves a thin layer of graphite behind. See if that helps with the primers dropping in easily.
Another thing you can do is buy a cheap post level at one of the big box home repair stores and tuck its inside corner against the pickup tube so you can make sure that tube is vertical when you pull the pin to drop the primers. That should mitigate primer cocking at least some.
