Thanks for the replies chaps, there's some great info and food for thought in there.
Neil's point is a good one – there's no requirement to engage the full face of the cutter, so even if the mill is struggling in some situations, the depth of cut and degree of engagement can be backed off.
I'll look in detail at the APKT insert mills, the inserts certainly appear to be a lot more sophisticated than the TPAN ones.
I'll also persist with the fly cutter, given the favourable opinions. David – I assume your reference to a "small radius" means taking off the sharp point of the cutter, which I guess reduces the chances of it chipping. I do have a bench grinder of unknown provenance – the previous owner of my house left it behind when he moved, but I have hardly used it. It runs smoothly and quietly, but the guides and guards are shot and will need some work.
What is the best source of carbide to mount in the fly cutter? Can you buy "blanks", or is it easy enough to grind down the ends of broken end mills or drills?