Used 2.25 mm needle(s) for toe, heel and sole with 2.5 mm needle(s) for the top of the foot and the leg, i.e. 2.5 mm for cables and 2.25 mm for stockinette and the slip-stitch heel. I found that using 2.25 mm for the whole of the foot made the top of the foot too tight and pulled-in. This way the stretch of the cabled portions is similar to the rest of the sock.
Started toes, two socks at a time (so that I get the lengths of foot and leg the same on both socks) on an 80 cm circ (magic loop). Changed to a 2.25 mm 60 cm circ for the sole and a 2.5 mm 60 cm circ for the top of the foot (two circs), still two socks at a time. Knit the cabled legs of the socks using a 2.5 mm 80 cm circ (magic loop).
The added advantage of doing the cabled areas of the socks on 2.5 mm needles is that cabling without a cable needle is much easier on 2.5 mm needles than it is on 2.25 mm needles using this splitty yarn. I do not use a cable needle these days because I do not have one smaller than about 3 mm and also because I find it too fiddly to deal with a losable loose needle, which is also why I prefer circs to DPNs.
This yarn may have been cheap at my LYS but it is not holding up at all well to the prototyping process of knit, frog, knit, frog, reknit, frog, knit it again and so on. It is becoming thinner and more splitty the more times I frog and reknit. Hopefully I have finalised the design and techniques now and I will not need to keep performing those iterations!
It turns out that 2.75 mm needles are not large enough for the leg. Frogging again. I love this design but am having no end of trouble making them fit. Next time I will try 2.75 mm from the heel flap onwards and then 3mm needles from the start of the leg. Or something. Or give up for a while. Maybe until I have some mono-colour or tonal fingering/4ply-weight yarn more worthy of this design.