Does the picaxe contain a max232 chip? Because from the datasheet, the threshold voltage is 1.xV. +-8V seems way more than sufficient to trigger it. Also, typical output voltage swing for the transmitter is +-8V, and I do usually get those figures, at least on my programmer, and still it works flawlessly on my laptop thru convertor.
Anyway, the point is, you may be chasing the wrong tail. Try another usb-to-serial convertor. There are known cases where certain models of convertors simply refused to work.