Tenor guitar — adjust nut file size choice

Ulsinus

My new guitar is strung with the following light gauges:
10 thou
14 thou
21 thou (wound)
27 thou (wound)
I need to lower the action at the nut. (Bridge height is ok. Truss rod properly adjusted).
Decent nut files are expensive.
MusicNomad do a range of sizes at £23 a pop.
I don't think the Hosco Double Edged Nut Slotting Files Electric Guitar Set would work.
Grateful for advice as to the best to proceed for the least cost.

Ulsinus

Oh and it's in 'Chicago' tuning ie DGBE.

ICBM

You should be able to find a half-decent set with enough of a range of sizes - bear in mind you don’t need (and actually shouldn’t use) the exact sizes, the slots need to be slightly larger than the strings. If cut cleanly with a smooth rounded profile they can be substantially wider and still be right.

Ulsinus

ICBM said: [...] bear in mind you don’t need (and actually shouldn’t use) the exact sizes, the slots need to be slightly larger than the strings.

Thanks ICBM.