The OP closed gate problem is a good example; the only solutions proposed to solve it with Con relies on the hypothetical existence of an underwater passage completely filled with water, long enough to justify using Con instead of Str (the ability normally keyed to athletic activities) but short enough to be traversed.
So is the expectation that in the next edition a player should be able to call upon any of the six abilities in any given situation? That seems like quite a stretch to me.
Meanwhile you can use, for example, Dex to open the lock, to climb the wall, to steal the key, to slip through the bars or to enter behind someone without being seen, just to name a few examples.
Sheesh if you really want examples of ways Constitution could be used to get inside a guarded manor house, here ya go:
1. Ditch your gear an hire on as a porter lugging goods into the manor courtyard or a sedan chair carrier for one of the manor nobles.
2. Engage an off duty guard in a drinking contest.
3. Hang on to the bottom of a carriage leaving town bound for the manor.
4. If the noble is an enemy, you could turn yourself in and just endure torture/beating, as part of a larger plan.
5. As a group somehow make the environs of the manor inhospitable (eg. control weather or start a fire), and while the manor is being evacuated the party sends in their toughest member.
6. Show the manor lord's rebellious son/daughter a "good time".

7. Have a wizard cast a polymorph spell into a housecat or a horse which requires a constitution based system shock check.
8. Aerial drop from a high tower/tree or while flying overhead - use CON to brace for fall (hey if you can use Dex to climb insead of Str why not?)
9. Engage the manor's guardian in a "game of wits" a la Princess Bride.
...and...
10. Hold your breath thru the stream feeding the manor's well.