As is often the case, after stepping away from the problem for a bit I came up with a simple solution:
First, secure one side of the gantry to the table (or have a friend hold it). Next, apply power to the machine, but engage an e-stop. Now take a long square (I used a drywall T-square) and place the short side flush against the side of the gantry that is secured so the long side is pointing across the table to the unsecured side. Make sure that one edge of the long side is lined up with some landmark that appears on both sides of the gantry (I used the vertical edge shown in the above pic). Finally, go over to the unsecured side of the gantry, manually deflect it until the same landmark is lined up with the appropriate edge of the square, and then release the e-stop switch to apply power, thus locking it in.
Granted, this is not a super-precise method, but given that you’ll probably get your deflection down to less than an eighth of an inch over the entire width of your table, it should be close enough for most work.
Ok, back to making Kickstarter rewards!