Yes this is a bit odd, but you have not used a closing repeat at the back of the 1st time ending which is what the player is expecting to see. I cannot remember ever seeing a 1st time ending without a closing repeat, they might exist but I am not sure they are very common because generally you can simply use repeats (unless it has a complicated form or nested repeats etc.)
So we did not check the behavior of the location of the double barline for this instance.
Just to make it clear to anyone else following this thread, here is a way to have the form, by changing where the opening repeat and segno are:
(I think this is what you would have done already Jack?)
BBB more correct - Borodin-Forrest-Wright