JNW - I can't tell from your two posts whether you're a Browning Citori fan and want one in 16GA with double triggers ONLY or if you're open to other suggestions. If you are a long-gone Browning Superposed fan, I understand FN Liege will make you one in 16GA, but be sure to be sitting down when you get the price quote. For the amount of money involved, maybe FN would even install double triggers. My comments which follow also tie into other poster's comments and are offered FWIW.
From the flavour of the other responses, you're in for rough sledding getting or altering a 16GA Citori to the double trigger configuration. The FAIR I ordered summer AD2002 from Brian Dwyer/Gunmart Brockville Ontario (now deceased) came in as requested in 16GA, English hand, double triggers, and slightly longer LOP and barrels than listed. Also standard was a slight cast-off for a right-handed shooter, nice Turkish walnut, and a blue plastic combination locked carrying case with four or five choke tubes. Your local dealer might be able to "special order" such a piece for you, and he might not. For MY special order 16GA I paid the normal price the same as what he had in stock on his shelf. You don't even get a NO, without asking.
I don't know for a fact, but suspect Isodoro Rizzini (aka F.A.I.R.) supplies barreled actions for his brother B(atista) Rizzini and for Caesar Guerini, and likely others too.
I ran afoul of the late Michael McIntosh's 16 and 28GA silver tongue, and ended up with FAIRs in 28GA (first) off the shelf, and then 16GA ordered in.
I completely sympathize with "double triggers", and with the English hand I enjoy an inward "Kodak moment" just holding it.
Hope this helps.