TLEs make everything harder, so try to avoid using them whenever possible. For the ISS, you should get ephemeris data from https://spotthestation.nasa.gov/trajectory_data.cfm and propagate with something other than SGP4. Please don't use or alter TLEs for the ISS.
It is certainly possible to update a TLE based on new measurements, because the U.S. Space Force does it for thousands of objects every day. However, unlike TLEs themselves, the software used to do that is not available to the public, and neither are the data sources. The amount of work it would take to reconstruct those tools is immense: other answers on this site which describe parts of what you need to do include PseudoTLE creation , How to generate TLE file? , and In MATLAB, Computing a new TLE/orbit following a delta-v impulse?
I haven't used GMAT in several years, so they might have done some of that work for you, but I don't know. On the other hand, OreKit seems to have made some progress along those lines, so maybe GMAT isn't too far behind, but I wouldn't bet on it.
If you are hell-bent on doing it the hard way, the core thing to keep in mind is that the only adjustable parameters of the SGP4 propagator are the 138 characters of the TLE itself. You can't change the degree of the gravity model, you can't change that it uses solar and lunar perturbations but not other planets, you can't change how it computes solar and lunar perturbations, you can't change the integrator (because it was done by hand! the only computation it does is a lookup table of Taylor expansions of analytic equations), you can't change the atmosphere, you can't change that the ellipsoid is WGS72, etc.
The only things you actually get to change are the numbers in the TLE, and you must never forget that they are mean elements, not osculating ones. One parameter of particular interest is called "B-star", which appears formally in the equations as a drag coefficient, but in practice has very little to do with drag, and is instead determined primarily by the differential corrector trying to fit the trajectory computed from the elements to the measurements.