How can I calculate the relationship between propeller pitch and thrust?
The geometric pitch ($p$) is simply the distance that a point on the prop would move forward in one rotation, if it's gripping in a solid medium. You can derive the pitch speed via this geometric relation if you wish, but I would caution against inferring performance from this number. Instead, you should consult propeller, engine and aircraft performance in their entirety.

Using your provided data, let's see if everything fits. We assume:


Prop RPM of 2200
Top cruise speed ($V$) of 125mph
Prop diameter ($D$) of 2.36m (from Wikipedia on SE5a)
Prop pitch ($p$) of 1.75m
Wing area ($S$) of 22.7 sq.m (from Wikipedia on SE5a)


From this reference, the reference pitch angle/blade angle ($\theta$) by convention is measured at 3/4 of the blade radius, and can be related to pitch via:

$$\theta=\tan^{-1}{\frac{4}{3} \frac{p}{\pi D}} \approx 17.5deg$$

The advance ratio is calculated, with $n$ being the prop rate of rotation in round per seconds:

$$J=\frac{V}{nD} \approx 0.65$$

Using the plot below as a rough reference, which is predicted for the McCauley 7557 propeller, gives a thrust coefficient ($C_T$) of 0.06.



Ref: http://webserver.dmt.upm.es/~isidoro/bk3/c17/Propellers.pdf

Now the thrust coefficient is defined as:

$$C_T=\frac{T}{\rho n^2 D^4}$$

where $rho$ is the air density and $T$ is the propeller thrust.

For level flight, thrust equals drag, and we can back calculate the drag coefficient:

$$C_D=\frac{2C_T n^2 D^4}{V^2S} \approx 0.07$$

This is high enough to be well within the realm of possibility for a biplane (if it's too low, then it's an indication that the performance numbers do not jive). For reference, Cessna 172 has a total drag coefficient of 0.032 at 122kt at SL. In conclusion, I would say that your numbers check out in the back-of-envelope sense.