Spanner, thanks for getting in on the conversation.
The way you're describing it is exactly how I ended up setting the floats, with
the float valve fully seated and the tang on the float assembly just barely touching the spring-loaded pin in the center of the valve. The way Terry described worked fine for me, as the spring in the valve is strong enough to hold up the float assembly without being compressed. Also, setting it this way made the measurement from the bottom of the float's end farthest from the pivot to the seating surface on the carb body just about 12.5 mm, as the shop manual said it should be.

You're post confirms for me that I ended up doing it right. Thanks again!
One thing that I noticed is that if the tangs are not set at the same heights in relation to their respective floats then all bets are off. The floats could all be set to the same heights but the valves could all be in different states of closure!