Upside down, you're asking the upper arm of the mainspring to do alot in pushing the self-opener foot with enough force to tilt the muzzle of the bbls upward.

I don't think they had Gang'sta Style Shooting in mind when they designed the system.
Maybe if the bbls were cut to 12" or so, it might be able to flip them up. Less leverage working against the mechanism that way.
The J. Purdey Auto & Burglar Model self-opener. Just the ticket for those tight situations

Enjoy it as it is. Better to be upright and still shooting!