Thanks for the replies.
I managed to sort it - the cause was very simple, as was the solution. I'll post it up here in case anyone else finds it useful.
You know the blue, self-adhesive "wrapper" that Sony puts on the battery? Well, the edge of where it wraps around the side of the battery was catching on a sharp edge of a plastic moulding near the front on the inside of the battery compartment. Using the tip of a very small watchmakers scredriver, I was able to gently push the battery towards the rear of the machine (not back into the battery housing) to disengage the wrapper from this plastic edge, and then the battery slid out like a charm. I rubbed down the wrapper with a fingernail to make it stick well to the battery, and I used a very fine tipped scalpel to shave away the sharp edge on the inside of the battery compartment (it's right at the entrance of the compartment, on the "front of the machine" side of the battery slot - hard to describe but easy to see when the battery is out). I only had to shave away a TINY amount of plastic - no need to go over the top. And now my batteries slide in and out like a charm!
Sorted.