Without the ground plane, if you really want to analyze it, it turns into a
very messy 3-dimensional problem, involving a lot more space than you need
to worry about when you have solid planes. I wouldn't even know where to
start. Everything interacts with everything else. Which is, of course, why
boards without planes don't handle faster signals; and may not have worked
well even with the slower signals of years ago. Forget analysis and go for
lab measurements.
I'd suggest doing what you can to regain real ground planes. If you can't
add layers, try doing a ground "fill" on one or both sides of the board,
with lots of vias to connect them to one another.
Andy
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