I haven't tried this with Juniper/Barclay, but in my experience at other banks with other airline cards:
They usually can't "down-convert" a card without issuing a new account.
How long before the annual fee comes due for you?
If it's enough time, I would suggest you ask if you can open the lower-cost one (or any no-annual-fee card they offer) and then "consolidate" them so as to apply your credit history from the MW World to the new one.
I've been able to get this done so many times, I sometimes get confused. I recently called Chase to ask about cancelling a card I've only had for a couple years, and they told me why do I want to cancel it when it has credit history going back to the 80s? I turned out I'd forgotten I'd already consolidated it with another one (that I had indeed had since the 80s)!
