Can I set up a First page template to show the first bar of a flow on the next page?

I have been trying and failing to create a First page template that will show only the flow header, and postpone the first bar of the music to the top of the next page.

Why would I want to do this? My current interest is in band scores where it makes sense to treat a programme as a project and each piece as a flow. The flows are typically short (one or two pages) and offer few good places to put page turns. So when the piece fits on one page, I don’t care whether that is a left or a right page, but when it needs two pages or more, I want the first two pages of music to be facing pages. I have seen choral répétiteurs make miraculous snatches at their piano reduction scores, but I think any wind player attempting something similar would most likely just knock the music stand over. And I can’t get my printer to do fold-out pages with sticky tape.

It would also be useful to put the flow header with the flow title on the otherwise blank page before the first bar, rather than above the first bar.

Can I make a page template do this?

I can get most of what I want by inserting a custom blank page before the flow and retyping the info in the flow header in a text frame; but reordering the flows in the project messes it up completely.

The other alternative is to make one flow per project, but it is helpful to be able to set project wide engraving options only once, rather than trying and failing to keep different projects in line with one another.

I’d welcome suggestions, including the suggestion that this is not something that Dorico really wants to do, which is why I’ve been finding it difficult.

Flow Headings are linked to (actually positioned within) Music Frames, so you can only have a Flow Heading if there’s music attached.
An alternative method would be to build Text Frames into the Page Template containing the same tokens as those used in Flow Headings, but you run into the same potential problem: {@flowTitle@} (and all the other flow-linked tokens) can only resolve if Dorico knows which flow’s information to pull in, and Dorico only knows that if the music of that flow is on the same page.

I think I’d build a title Page Template that has the name of the whole book on it, then Insert Page Template Change to push the first flow onto a left page. Then for subsequent flows I’d build a blank page template (either entirely blank or with any of page number, running header containing the layout name, text explaining why it’s a blank page).

You certainly could use the fields from Flow Headings on your blank page, but it’ll be a case of either manually copying and pasting information into them or replacing {@flowtitle@} (etc.) with explicit {@flow1title@}, {@flow2title@}, {@flow3title@} tokens.

At the risk of duplicating some of what Leo said…
Dorico cannot automatically summon a flow title into a page with no music on it (as I believe you have discovered). But you can use a token for {@flow1Title@} altering the index number for each flow.
You could make a separate (title) Page Template for each flow. I wonder whether, when you switch the position of the flows, the flow index will change such that you would not have to change the title page for that flow unless a one-page flow replaced a two-page flow.
Making the separate Page Templates is an investment of time, but the Page Template Set could be exported for use in similar projects if you do this sort of compilation often.