It seems to me that this is pretty much the same as making joints in
kitchen worktops. For these, biscuits and clamps work very well and
are very easy to do with a router.
The tricky part about the long tongue would seem to be making sure the
fillet is a good fit, so perhaps there's a compromise of routing a
groove along each board using a biscuit joint cutter, then stacking
the biscuits along the groove.. Be a good idea to hold the boards
together 'laterally' though, somehow (if you got some of the Ikea
worktops, a kitchen clamp would be just the job as they're thick
enough.)