Originally, I thought perhaps you could use something like the "Flush Ring Catch" as shown on page 559, figure 'M' of the 2007 West Marine catalog. But then my Dutch heritage kicked in. How about making up a channel, out of wood, affixing one to each end on the underside of the lids, with a piece of wood to slide outward in it. Then, route a slot in the lid, just big enough for your finger to go through, and will a similar hole in the piece of wood, you could slide your "latch" back and forth. Or you could route a slimmer hole, and glue a brass pin in the wooden "dog". The channels I am trying to describe would look like those on one of those wine glass racks, where the glasses hang upside down. If you epoxied all the wooden parts up for moisture sealing (which you've probably already done to the birch ply) you could slide them out and give them a rub down periodically with paraffin and I'd bet they'd slide just dandy.
If you didn't want to make the channels out of wood, you could use the window channel WM has on page 582 at 8' for $26, instead. But I think a trip to the lumber yard, in the molding department, will probably reveal something you can just cut and screw/glue down.
I find that the WM catalog brings out the thriftiness in me like nothing else.(g)
“Scientists are people who build the Brooklyn Bridge and then buy it.”
Wm. F. Buckley, Jr.