User selectable background that doesn't blink

Question

Is it possible to have a flash animation, inserted in slide 1 (or on a master slide) that runs continuously in the background, without reloading or restarting as you go from slide to slide?
I'm building a course in which the user can choose between two backgrounds. The chosen background should appear continuosly as the project moves from slide to slide.
At the start of the course, the learner chooses a background... say, wood or stone.
I've tried:
1.) I built a Flash swf that does this: offers a choice, then fills the screen with the chosen background and stops.
     a. I put the swf on a master slide.
        problem: it reloads on each slide, and asks the user to choose again.
     b. I put the swf on the bottom layer of the first slide, and set the TIMING to Display for Rest of Project.
          problem: It displays on TOP of everything.
2.) I put one of the backgrounds on the master background, and used advanced actions to hide and show the other one, based on a variable. It required the second image to be present on every slide, and the advanced action to hide/show all of them each time. It works well if the second image is being hidden.
     problem: if the second image is being shown, it shows the background for a millisecond, and then shows the second image. It blinks on each slide. It's not continuous and annoying to the learner.
Can anyone think of a way to get a continuous, non-blinking background image (across slides) that is user-selectable?

Answer 1

Thank you Rod Ward for your prompt, correct, and encouraging reply.
It worked. The slides with the Rest Of Project background need to have their Master Slide property set to None.
Here's what I did:
slide 1 - would you like background A or B?
     A is a button that jumps to slide 2.
     B is a button that jumps to slide 3.
slide 2 - has image A with duration Rest of Project. (uncheck Place on top)
     On enter slide, I set a custom variable to "A"
     On Exit slide Jump to slide 4
slide 3 - has image B with duration Rest of Project. (uncheck Place on top)
     On enter slide, I set a custom variable to "B"
     On Exit slide Jump to slide 4
slide 4 - On enter slide, if custom variable = "A" hide B, show A; else hide A, show B.
     (You wouldn't think I'd need this, but the B background would reappear even though I "jumped" over it, and stay on top.)
subsequent slides -
     - On the Enter action of a given slide, I can us Advanced Actions to hide/show graphics (and attached sounds) based on the user's intial choice.