For decades, I had to read such scores as a conductor, singer and player (G&S especially). I confess to never having tried to emulate this notation in Finale, instead, putting it into modern notation.

Finale can do what you want but it may take a little work on your part.

Start here and look at Nonstandard Key Signature

https://usermanuals.finalemusic.com/FinaleMac/Content/Search.htm?q=%20Nonlinear%20Key%20Signature

You can select any other symbol to replace the quarter rest if contained in the font you are using.

https://usermanuals.finalemusic.com/FinaleMac/Content/Finale/Document_Options_dialog_box.htm?Highlight=backwards%208th%20rest

If the symbol you need is not in the font you are using, it's possible to create your own.

Some of these things are basic to Finale. If you've not gone through the tutorials yet, now is a good time to do so.

The old quarter rest is in the Bravura font, but I have no idea if the rest of the font is compatible with Finale.

It's also shown in the SMuFL table. https://w3c.github.io/smufl/gitbook/tables/rests.html 

But all of this is way over my head!

Ha! I tried to make Bravura work in Finale just yesterday but am unable. Frankly, I didn't try very hard.

There'a a bug with Bravura and Overture 5.  (#) displays as 6. I was trying to figure out if the problem was the font or Overture.

It's also shown in the SMuFL table. https://w3c.github.io/smufl/gitbook/tables/rests.html 

Then November 2 should also have it.

Right. And it's also in Fravura.

But November is about  € 80. While it's easy to spend OPM, I don't know if Derryl is up for that! I guess it would depend on his project.

Does the custom key signature appear on every system? If not, I would just drop it in as an expression. Even if it's a few systems, it might be the easiest way.

Since we've not heard from the OP, not much else to do except speculate. Whether or not to spend money on a custom font or create a custom symbol for the use - or even use a text expression and hide rests or...

It all depends on the scope of the project and what one's time is worth. Big difference between transcribing Ivanhoe and a Vaughn Willams hymn tune.

… Does the custom key signature appear on every system? If not, I would just drop it in as an expression. Even if it's a few systems, it might be the easiest way …

You can also add the extra key signature accidental with the Staff Tool, as a Staff Name or as a Staff Group Name.

In that way the accidental will automatically appear on any system you need.

How would you do that, Peter?

… How would you do that, Peter? …

You can give a staff or a staff group any name, in any font.

To get a sharp accidental, use as the Name the character ‘#’ from a music font in size 24 Points.

You can set the #’s Positioning precisely, Horizontally and Vertically.

To get a Staff Name only in a specific region (not in the entire document), use a custom staff style.

To get a Group Name only in a specific region (not in the entire document), customize the group’s measure range.

Thank you for all of your input.

The client will have many full page music documents and I would have the same problems many times over.

After I informed my client of potential difficulties with the backward quarter rest, double key signature, and old English text, he decided that we would be better off to put into modern music format and text for his book illustrations (as Mike alluded to in his post).

Whew!!!

Scoring for British bands requires all instruments except for bass trombone to be in treble clef.  How do I get the wizard setup to create trombone, baritone, euphonium, Eb tuba, BBb tuba to be in treble cleff, with appropriate key signature?

Set it up by choosing the instruments you want, from the wizard. Then, you can go to the score manager, and adjust the clefs and/or transposition as needed.

Once you have done that, save the score as a template. Then, you will have it already set up, the next time you want it.

Thanks Mike... that will work.