UPDATE - Due to family issues last weekend (and me being temporarily located over 150 miles from my bike), this afternoon has been the first chance I've had to take a look at my bike since first posting and I've now started to try and use you guys' expertise to help my diagnose the cause of my problems. I think I'm getting to the bottom of it now, but it's too late and too raining to go out on the bike to test it, so I'll have to wait until tomorrow to be 100% sure.
Just so you can see, here's a picture of the damage that was done to my inner tubes:
It may not be immediately clear from this photo, but there's actually two holes right next to each other there, but the second one hasn't completely cut a full circle out of the tube and the rubber has folded back over the hole.
Luckily I found the other two punctured tubes still in my garage (hadn't thrown them away as I thought) and was able to quickly verify that all three had similar holes and in the exact same location - at about 5 o'clock when the valve is at the top (or 7 o'clock, depending on which way you look at the wheel). Using that I was able to check the tyre in that location using cotton wool and found no foreign objects that might have been causing a puncture and also could not find any abnormalities in the rim tape by sight or feel.
However I did find a small cut in the tyre at about that location - it didn't look particularly big from the outside and I swear I've got at least two others elsewhere on the tyre that are about the same size. Below is a photo of said cut and considering I've tried stretching out the tyre for this picture to make it more visible, it still doesn't really stand out.
However, when I checked the inside of the tyre at this point, it did look a lot worse for than on the outside (unfortunately couldn't get a good photo of this). It still felt fairly smooth when running my finger over it (inside and out), but the cut looked a lot bigger on the inside. This suggests that the people on about a herniated inner tube poking through the tyre could possibly be on to something, especially if it only showed up when at higher pressures and when I had my full weight on the bike. Remember that my first puncture was fixed at the side of the road and I used a CO2 canister to inflate and this probably only gave me 60-70 psi, which was enough to get me 40 miles and home - the run of punctures only started when I emptied that and used my track pump to put me up to my usual 100psi.
So what I have done now is to swap the rear tyre from my spare bike to this bike - it's also a Gatorskin, although it is a 23mm instead of the 25mm I was running previously (and I still have a 25mm on the front wheel), changed the tube following all advice in this thread and have inflated it to 100psi. Wheeled the bike around the garage and it seems fine, but as I said, I haven't ridden it properly yet and won't until tomorrow, so watch this space.