How can I manually organize photos within an album and then transfer them so that they stay in order on another device?e?

There are 3 ways you can do it:

1 - set File Name to Album Name with Number

2 - set File Name to Sequential

3 - set File Name to Title after adding prefixes, 01-, 02-, 03-, etc. to the Titles under the thumbnails.

Here's another approach to that:

1 - put all of the Photos you want to export into an album and sort manually as you want them.

2 - select all of the photos in the album, run this AppleScript, Batch Change Title to Text w/Padded Sequential Numbers, on them.

Now you an export batches of photos from that collection and have them sort as desired in the Finder.

The script compiled as an application can be downloaded from this tutorial site:  P01 - Applescripts from Photos’ User Tips Compiled as Applications

When you leave Photos you lose the sorting ability that the app has.

What you can do is rename the files, which is what the Finder is organising on, to match the sequence you prefer.

File -> Export and in the Export dialogue choose Filename -> Sequential

If you want to use the title you have given in Photo as a filename, then simply choose Title instead.

I think that if you change the prefix for each import the order might be preserved. So, first import would be prefix 1, second import would be prefix 2, third import would be prefix 3, etc. I haven't tried this, but just thinking that it might work. You might need to add sequential numbers in front of each title as well.

-- Rich