Most of the grease guns I have have the little notch near the end of the rod when it's pulled all the way out, but you have to get it ALL the way out to latch it. I clamp the tube part in the vise, then pull the rod and latch it, pop the top off the new cartridge and slide it in, screw the top on the gun then slowly let the rod back in as I pump the handle to get the air worked out. I never have a problem getting all the grease out this way, the cartridge is bone dry with just a bit left on the plunger when it's time to change it.
But, that said, I also vote for a new grease gun, and buy a quality one - it'll last longer and work better. I've bought those $8.99 ones and they mostly work OK, but a well made $34.95 Wagner will last a lifetime and be easier to use. Life is too short to use cheap tools.................