Martin,
that's a real pitty. Unfortunately I don't see a way to use e. g. trigger inputs or other digital inputs as an encoder input. The only thing I can think of is using the DAQ board to read the encoder position and then generate an analog output signal, that is proportional to the position and connect this signal to an analog input of the 7344. This analog input could be used as gear master for an axis, too.
Still, I don't like this idea very much due to the fact, that you could run into some signal noise issues and that the analog inputs of the 7344 provide only 12 bit ADCs, which gives you only a travel range of +/- 2048 steps. Of course you could amplify this range by using a higher gearing ratio, but this would result in quite rough moves, but depending on your application this still might be an option.
So, just to make sure: Are you running the axes in closed loop mode, so that there are no encoder inputs left?
The easist solution would be to use a board with more axes, like the 7356. Is this an option in any way? If yes, you may ask your local NI branch for a hardware upgrade and they should be able to offer the board at a much lower price.
Regards,
Jochen