…would be be strong enough?
Give it a try as you say.
Search for ‘3d printed change gear’ to learn of other people’s experiences.
In subtractively-machined gears, the tooth root is a byproduct of the cutter shape. In additively manufactured gears, you can increase the root fillet to the maximum before interference takes place, thus greatly increasing the tooth’s bending strength. As long as your CAD program offers this facility… FreeCAD does offer this.
If you are making something like the Thingiverse item, do not be tempted to make the inner profile as an internal gear as the fit will not be good – you have to subtract an external gear to make the internal shape.
Make a small gear to start with (possibly including the centre spline detail) and place it in the drivetrain such that it is the most highly loaded one in the train.
My guess is that would be directly on the leadscrew with the overall ratio being set up for a very coarse thread (i.e. 1:1 or greater ratio between spindle and leadscrew). For testing, it does not need to be a ‘real’ thread – if the ratio happened to 3.268 tpi, that would be OK.
Give it a torture test and see how much abuse is necessary to make the gear fail.
A loctite fit is easier to achieve than an interference fit. Back it up with a Dutch key if paranoid.