Well, that's all extremely informative. Many thanks for the detailed responses. It was a hard, expensive and ultimately destructive lesson to learn. I'm intrigued by Macdrone's suggestion to simply snip the axials and solder new caps onto the existing leads. That seems the safest route in my book. I'll also be getting a new soldering iron on techknight's advice. This one cost me about £20 and is indeed a single-temperature device.

I have a hot air gun, which I used initially, but I should have used it in tandem with the soldering iron. Here's a question: With the axials, do you only tend to work with one side of the board (i.e. underneath) when working the cap out or do you also heat up the entry points on top? I think part of my problems with exposing vias was due to using the soldering iron up top to try to heat up the entry points of the axials. Also, what's the best way to clear out the hole once it fills with solder? Is it simply enough to heat up the solder to drop the new lead in? Do you come at that from the top or bottom? Many thanks!