The easiest way is to take a cleaning rod and jag of the proper caliber for the barrel and place a tight fitting cleaning patch on it. Run it into the barrel and stop it just short of what you wan't to measure. Then when the casting cools where you can handle it comfortably, pop it out using the cleaning rod and pick the patch off the casting. it will be stuck on the casting but can come off easily.
What you get when you include the riled part of the barrel is the same as having a bolt screwed into a threaded hole. if you try to drive the bolt out without turning it, it goes pretty hard. The barrel part of the casting acted like a bolt in a threaded hole ( the barrel). When you pounded on it, the soft casting material slugged up and got even tighter, making it worse. The easiest way to get it back out ( if it's stuck) is to melt it out, not pound it out . You didn't say how long you waited before you tried to knock it out. If you wait very long, it will swell up and get tighter. So extract the casting soon after the barrel cools to the touch and keep the rifled part short. The casting is very soft so knock it out with minimum force onto a padded cloth to keep from bending it or putting dings in it.
If you can find a cheap tin cup, they work well for melting and storing the cerrosafe. A pop can is pretty flimsy and has no handle. I just drop the casting into the cup and leave it like that till I need it again.
When measuring, use a known accurate micrometer if you really want to get a good reading. I don't use indicating calipers as they are seldom accurate within a thou. unless you buy a good set and pay lots of money for them. You can check the accuracy of your mikes or caliper on a standard that comes with good mikes. Or, I have a set of Jo blocks and use them to check my measuring tools with. I have a set of Mititoyo digital one inch mikes. They read out to plus or minus 5 millionths of an inch. When they are that sensitive, you can see them change over time as the temperature of the mikes change. It's a simple matter to just hit the re zero button and be accurate again. Indicating calipers are large and can change a whole lot more just from temperature changes. So don't rely on them if you want to measure down into the .0001" range.
Once you do a couple of casting you will find that it is pretty quick and easy if you do it correctly. Keep us posted on how it works out for you.