While we're tossing out ideas, here's a couple untested concepts - both
would require some effort...

1. How about not trying to move the big lumber, but the tool instead?
I might have missed this suggestion with all of the others so far... You
used a similar technique with the planer.
- Clamp your boards solidly together, 'joint' side up
- Create a 'runners' out of smaller boards that you can mill accurately and
locate them on each side of your lumber
- Create a carriage for your router that slides along the rails, but moves
back and forth as you go down the length trimming both boards flush -
Accuracy here is very dependent upon your sled setup

Wood magazine suggested a similar setup for those who had a router, but not
a planer, but it might work here

2. Another option would be to not try to cut through the entire piece, but
leverage off of the dado that you plan to use for the spline, a couple
different flush trim bits, and sacrificial splines.
Note: the flush trim bits must be the same size OR the one with the bearing
on the router side must be larger
- Cut a dado in both of the long boards
- Cut a (hardwood) spline and joint or plane it to a slightly thickness LESS
than the depth of your dado
- Use your router and a flush trim bit (bearing on the end of the bit) to
make a clean edge on both sides of the FIRST board
- Cut another spline that is just a little larger than the depth of your
combined dados PLUS the width of your second flush trim bit (with the
bearing on the router side)
- Place the sacrificial spline in the FIRST board
-With the second flush trim bit (with the bearing riding on your lumber) cut
a groove in the spline deep enough to use as a reference for the first bit
- Either move the sacrifical spline to the SECOND board or attach them
together (depending upon the size of your bit)
- Use the groove in the sacrifical spline as a reference to cut a matching
face to the original
- You may need to repeat this process for the second part of the SECOND
board.

My $.002