Answer: A solution that doesn't change the rules of the game is to provide all players with a list of all valid two-letter words. I have tried this methodology and it works fairly well for equalizing the playing field which is part of the subtext of the question.
Explanation: One of the underlying problems of your question is the line between casual Scrabble players and those that do (or have at some point) taken it more seriously. I was a casual player up until the point where I discovered an PC version of the game that had a training mode. It grilled you on two-letter word combinations until you had them all memorized and then started grilling you on three-letter word combinations (I never memorized all of those.)
After this, my Scrabble playing was never the same, nor was it strictly much of a contest anymore when playing against "casual" players. The trick wasn't playing one ridiculous two-letter word, it was find a way to play one long word alongside another with 4 or 5 two-letter words mixed in, making use of several that you would dub ridiculous.
The reason providing the word list works well is because you are really only helping with a small subset of lesser known two-letter words. This takes the advantage away from the non-casual players and forces them to rely on their other Scrabble skills...or at least forces them to start practicing their three-letter words.
The other consideration of this method is that all players will eventually have learned the two-letter words well enough to stop providing the word list as it has done its job and helped all players be on "equal" footing again.
AA AB AD AE AG AH AI AL AM AN AR AS AT AW AX AY BA BE BI BO
BY DE DO ED EF EH EL EM EN ER ES ET EX FA GO HA HE HI HM HO
ID IF IN IS IT JO KA LA LI LO MA ME MI MM MO MU MY NA NE NO
NU OD OE OF OH OM ON OP OR OS OW OX OY PA PE PI RE SH SI SO
TA TI TO UH UM UN UP US UT WE WO XI XU YA YE YO
I have bolded most of the two-letter words that I would have not known for sure were valid prior to "studying". Feel free to do your own count to see how many words you get help from if the list were in your hands during play.
Here is a link to site that talks about allowed two and three letter words.
Here is a club list that has definitions as well
Also, wanted to give credit to Steven Stadnicki as this answer mirrors his suggestion.