Tooth stiffness is variable along the tooth. In order to avoid a local overloading, at assembly gears are set so that the contact at low torques is toward the small end and under load progressively goes along the tooth. This leads of course to a displacement of the resulting tangential force along the tooth. This displacement is function of the stiffness variation and the best is to analyze it with a FEA approach at least for one sample. Axial force depends on angles which will not change so much that their variation could influence the ratios.

If there is a mathematical defined law for the displacement I do not know try google and other academic sources may be some research was done and you find mode detailed information.

In general for different reasons teeth length is relatively short (i.e. the ration tooth length to cone generator line length is

Then consider 3 situations : forces at small end, in the middle and at the other end and see how this position changing will affect  life expectancy. Do not forget that you have torques as load so that tangential forces change according to contact radius.

Good luck, I think you would have to deduct the equations your self. First you mentioned bearings now you want profile influences. To make a short remark: torque is the product of a force and a distance in this case the radius between contact point and revolution axis. For a constant torque forces will depend on the contact position along tooth so they are variable. Now you have the the profile on which the force acts. You could consider every tooth as a clamped beam with variable stiffness and long with respect to profile height. The problem has to be solved by the theory of elasticity and geometry is not an easy one. Of course you could approximate the beam profile with a trapezoidal one but it remains complex this is why I suggested the use of FEA  which allows with a series of simulations the development of a relationship which shows at least trends. If you want to make the problem even more complex (it is more realistic) you can take into consideration the elasticity of the clamping zone which leads to a tooth bending and a slight change of the contact angle since the flank profile involute follows the tooth bending. I would be interested to see the results when you are so far.

To add a point for the gear (z2>z1) the wall on which teeth are clamped has to be thick enough if not the "plate" will also bend and increase the profile angle modifications.

On a conical (bevel) gear ? Or on a cylindrical (spur)  gear?

Attached sketch will explain why the distance is variable and thus the force = Consider that the torque applies ON THE SHAFT and if you consider a point contact (or even a line ,one) when it is moving along the tooth it is, on a bevel gear, at different distances (radii) with respect to the shaft center line.

What you wrote is valid in a section across both bevel gears and normal to the cone generating line but if this section moves then...

It is true that for design the bevel gears are replaced by spur gears with mean values for dimensions but you want to go deeper so that the model has to be adapted to what you aim at and your thought as well.

Thank you for the "small" correction.[(-:)] !