The shorter range for a 20 gauge is more fiction than fact. A lot depends on your pattern. You are dealing with less shot but actually firing it at a higher velocity than the 12 gauge magnums. My daughter's 20 gauge will kill any turkey out to 35+yards dead in it's tracks. At 35 yards it's still putting 10-15 #6 shot in the kill zone. She's shooting a Remington 870 youth with a Hasting turkey tube and federal 3" 20 gauge #6 shot turkey mags.

If you still want a 16 gauge check out any premium mag lead. Many of these are offered with buffered loads and function very much like turkey loads.

Federal Cartridge has 16 guage; 2 3/4"; 1 1/4 oz; 4,6 shot; 1260 ft/sec, buffered premium magnums.