If I understand you correctly, Measure 3 is a 3/4 measure with a double barline, and Measure 4 is a 1/4 measure, right?

Take a look at

Document menu > Document Options > Music Spacing

What is the setting for Minimum Measure Width?

You're right about measures 3 and 4.  Essentially I'm just putting a double barline part way through a bar of music.  As far as I know, I need to tell Finale that it's two bars, although musically it's a single bar.

Good idea to check Minimum Measure Width, but Minimum Measure Width is set to 0.  As I said above, the Fibonacci Spacing library doesn't have this problem.

It looks like you have found a shortcoming in the Tight Spacing library.

Instead of trying to fix the Tight Spacing I suggest that you try a Scaling Factor spacing (like Fibonacci spacing) with a lower scaling factor.

Fibonacci uses the Golden Ratio as its Scaling Factor.

To get a tighter spacing than Fibonacci, try e. g. a Scaling Factor of square root 2 (= 1.4142).

This is done in

Document menu > Document Options > Music Spacing > Spacing Widths…

Thank you for your help, Peter.  Indeed I am using Fibonacci spacing, and it's working pretty well for me.  I'll try adjusting the scaling factor.

I have a similar problem, but can't even get this far.... tempo is 3/2 but a bar is divided into one of 2 beats and another of 1, with a double bar dividing them.   The dialogue box for time signature on my version of Finale MakeMusic (2014) doesn't have the 'time signature to display' option.   Is this a version issue or am I pulling down the wrong dialog box?

… The dialogue box for time signature on my version of Finale MakeMusic (2014) doesn't have the 'time signature to display' option.   Is this a version issue or am I pulling down the wrong dialog box? …

Are you using the “full Finale” 2014, or are you using PrintMusic 2014?

Only the “full Finale” has the option of displaying a different time signature than the actual time signature.