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I am just brain drooling here in a short break. Not sure I thought this through very well, but was doodling for a few minutes based on the ellipse discussions. thinking a seat of the pants guesstimated error circle and most likely position.

It's quick,...a calculator eyeball method of a two point fix within an area of probable error.  With three it gets messy but visually might still help in a rush.

I have two LOP’s, and a DR position. Draw the perpendicular from the DR to the two LOP’s, same as you would if you had a single sight and a one point estimated position.

I draw an estimated error circle around each intersection of the DR/LOP perpendicular at the LOP.  The error circle is often the same diameter based on my typical accuracy in the conditions.

I connect the center of the two error circles and join them at tangents lightly for visual help if needed. In the pic they are small and separated, they may of course if my error estimates are good, actually overlap.

On the line between the centers carries my most likely position relative to my DR.  Side error (e.g. perpendicular to the line we drew) we conclude is smaller based on the limitations of our accepted error and the tangents.

The most likely position relates to the sum of the two error circle areas and the centerline between drawn earlier. If both are the same size, the most likely position is the midpoint.  If different sizes, it will shift toward the larger circle based on a simple ratio of areas.

We assume the ellipse must be within tangents, and the area we call the sum of the two circles. Using a uniform ellipse I can calculate the L quickly if I wanted.  So now I have L and W and area of the ellipse.  or draw one that looks like it equals the sum of the two areas. A little practice and you would get pretty close.

While obviously subject to some vagary, and with some crude assumptions,  it does seem to put me in a rational place in a few seconds of looking based on two LOP’s and with full acknowledgement of the DR.

I sketched it up adn attached it.  Does this have any merit, or is my tired friday brain simply fallen off the edge?

I'm afraid to push send for fear I'll realize  it was dumb later.......but oh heck...