Thanks all for the ideas!
One modification I'm considering is giving extra skill points to everyone except tier 1 classes. Most of them are Int-based so get plenty of bonus SPs that way, and the Cleric and Druid certainly don't need any help.
I like the idea of the skills that don't tend to get taken seeing some use. I'm not sure about Sleight of Hand, and I think Perform should count as an adventuring skill to any class which has Bardic Music or similar, and likewise Handle Animal for any class that gets an animal companion, but apart from that their list looks about right. I might implement this in addition to the extra base SPs or instead of it.
8? Blimey, it seems I'm worrying unnecessarily about 2...
I didn't think it would cause any major problems, but if there's one thing I've learned about D&D, it's that there's so often something important you didn't think of that it's always worth canvassing opinions before you make any changes.