In the system we are developing at the U of MN UAV lab we simply zero the differential pressure sensor before the flight and then apply a small scaling factor to the inflight readings. We use this code to compute airspeed. Note that the "pitot" variable is the current pitot tube pressure reading and "pitot_offset" is some average reading we collected at the start to estimate the zero airspeed reading:
float Pa = pitot - pitot_offset;
if ( Pa < 0.0 ) { Pa = 0.0; } // avoid sqrt(neg_number) situation
float airspeed_mps = sqrt( 2*Pa / 1.225 ) * pitot_calibrate;
float airspeed_kt = airspeed_mps * SG_MPS_TO_KT;
pitot_calibrate is a scaling value we determine from past flight data and for normal pitot tube installations usually has a value of around 1.1 for eageltree/3dr/mro style pitot tubes that are properly installed.
If you think through the formula a bit and plot it out, you might see that as your speed increases, the affect of calibration errors gets smaller.
Personally, I wouldn't over think the pitot tube calibration too much. Our hobby grade sensors aren't super great and there are lots of other sources of error in the system that could dwarf your careful wind tunnel calibration. My recommendation is to start with a simple calibration, do some flight testing, and then get your own feel of how well it is (or isn't working) and then you can decide if you want to concentrate more of your effort here, or call it good enough for now.
Follow on: I've found it useful to filter the pressure sensor reading before using it. Even on 'digital' pressure sensors you see quite a bit of noise. Filtering the signal a before using it has worked well for us. I started with a simple low pass filter, but then learned about butterworth filters (theoretically more optimal) so switched to those. You'd probably have plenty of compute power on your teensy to do some filtering if you decide you want to try it some day.
You are welcome to examine, copy, use any of our code (licensed with the MIT open-source license) if you find it helpful. I have my personal tiny slice of experience with these things, and I'm happy to answer questions about what I have done if it helps your project:
https://github.com/AuraUAS
And by the way, the fact that you are doing all this from scratch including the airframe design and construction is super impressive. Not many people in the world can assemble all the skills you need to this sort of thing in their head all at the same time! Wishing you continued good luck, good progress, and safe flying!