How can I modify an existing deck for a wide-open environment?
I think perhaps you are asking the wrong question.  

When I was going to an event for casual play, I'd normally bring more than one deck and I'd either ask for an opponent for a specific format or else ask the other person what format and break out the appropriate deck.  Obviously, I didn't carry a deck for every conceivable format, but if I brought my current standard deck, and an extended deck, and a "completely-casual-deck to play against beginners" I'd be able to find something "close enough".

If you really want just one deck to take to take to a gathering, then I would make a fast, solid aggro deck with some removal but no specific hosers (except just maybe in sideboard).  I would go with aggro over control or combo for a couple of reasons:


It always exists in about the same form in most formats, where control really needs to be tuned to the metagame to work right, so it can be broadly competitive.
You are describing a fairly casual environment of pick-up games.  Of course any competitive player would be happy to face combo or control, but it frustrates and surprises a lot of casual/new players.  So, for the sake of everyone having fun, I tend to run aggro in pick-up games and save combo/control for more competitive environments.


When building this deck to take to such an open environment, I would avoid anything that was designed as an answer to a specific threat (one with nothing for instance saw tournament play due to the metagame at the time, but it was an answer to one specific threat type).  I would also look more than normal at cards that could have multiple purposes (green has often had cards that would act as a creature, or kill an artifact).  Of course, such versatility often comes at a cost in terms of mana, but in that type of environment (might face anything, but generally on the casual side) that might be a fair trade off.

Finally, you can blunt a lot of the "random-deck" problems by playing multiplayer.  Even if you don't have an answer to a major threat, another player at the table probably does.