There are a number of options, here.
From her "usual" classes, the stretch to "primary melee" class is actually quite significant, there is always the option of summoned monsters to act as big dumb fighters while the PCs control them from behind.
Option 1) That which is called "monk" does not have to be the class "monk." Order of the stick illustrates this beautifully with Miko. Therefore, she can gestalt with basically any combination and simply call it "monk." This would be the course I'd suggest.
Option 1a) An excellent "front lines" scoundrel is the Malconvoker summoner. I would absolutely suggest making a gestalt malconvoker the primary character in what amounts to a solo game. For monk flavour, it's hard to beat Archivist || Wu Jen for the cloistered western/eastern monk feel versus the wire-fu feel. Making Archivist || Rogue would be an interesting twist on the theme, but would represent a monk who's rather more world-aware than her fellow monks.
Option 1b) As @Ace notes, Monk is a Tier 5 ("Capable of doing only one thing, and not necessarily all that well, or so unfocused that they have trouble mastering anything, and in many types of encounters the character cannot contribute.") class from the power scale. When considering a gestalt, the monk adds so little that the power level will be the level of the other class chosen. This is an issue because it would be so easy to overshadow the primary character with, for example a Ranger||Cleric (Tier 4, Tier 1). In a 2 player game, Having a Tier 5||whatever and a Tier 1||4 character presents a difficult challenge in scaling challenge difficulty. Call the swordsage a monk.
Option 2) To "balance" the monk with full BAB, give the monk tome of battle bonus feats. This will improve the monk's combat performance to that of a fighter, making it a slightly less horrible choice. From the perspective of the options, a monk with full BAB and an extra feat or two may be the equivalent of a ranger. It is likely that a monk thus enhanced would not be a completely forgettable part of a character. Remember, you're trying to match tiers with your character, to make it easier to have the "monk" take the forefront.
Option 3) If you like the power level of monk, and don't want to substitute other classes for it, eliminating either the free feats or the flurry of blows would be a way to adjust for the increased attacks or chance to hit with the BAB.
I personally recommend options 1a or 1b.