Mark
Sounds complicated. If you ever want/need to replace the infills, you will have to devise another method of attachment to put them back, if I understand your description and you have screwed up through the sole, before fixing the steel sole plate.
Given the time and skill you are investing in this project, I doubt that you will be treating it roughly, but accidents can always happen.
I have an old Mathieson coffin casting somewhere about, which I was given by my late Father in law. the front infill is beyond recall but the rear, overstuffed is a sort of bun shaped, and may need to come out. There aren't any obvious signs of how it is fixed in, but I must give some thought to this next year.
On my Bristol bronze mitre casting, I epoxied, but on the small brass and steel d/t plane I made several years ago, I went the KH route with a riveted steel pin, within a brass tube. With care and protection from sticky tape, I managed without dings.
On the current project, I will do the same, if only because I drilled all the cross holes in the side plates at the same time, when the plates were originally lightly riveted together.
I am not sure that it makes an awful lot of difference because the chances of you extracting the infill without major damage, is, i would think, relatively slim. If you think that you are likely to want to repair or change the infills altogether, screwing is your only option, but like you, I am not keen on any more screw heads on the sides than absolutely necessary.
Be very interested to hear from anyone else who has managed the extraction of infills without destruction.
Regards Mike