NavList:

You can definitely do this without plotting. Here's how I would get started.

One you have the subsolar point at the moment of your sight as lat/long, you can convert it to a three-dimensional coordinate plane, using an idealized spherical earth:

x = cos(lat)cos(lon)

y = sin(lat)

z = cos(lat)sin(lon)

Then, 90 degrees minus your corrected altitude gives you the angle between your location, the center of the earth, and the subsolar point. You can use the nice property of the dot product here; that is, [x1x2 + y1y2 + z1z2] gives you the cosine of the angle between them.

Each sight will then generate a pile of equations. Solve them all, to get your x,y, and z, then convert back to lat/lon

I don't know if there's a closed-form solution for this; it seems fairly likely, but if not, you're in the "guess-and-check" land of numerical solutions.

Apologies in advance if I've made a mistake or missed something obvious!