You should be able to use tie lines to “connect” the Broadcast Waves server I/O to the FOH console through the Dante I/O cards. These tie lines will be set up/routed on the Broadcast console.
For example, if you want to use use Broadcast Waves I/O channel 10 on the FOH mixer, you would use the tie line routing on the Broadcast console to route the Broadcast Waves I/O card channel 10 to the Broadcast Dante I/O card channel 100 (or whatever channel you wanted that was above the normal input routing from the FOH to broadcast console). You obviously need to make sure the routing between the FOH Dante card and the Broadcast Dante card is also set up correctly in Dante Controller. Then on the FOH console, you would simply insert FOH Dante I/O card channel 100 (assuming 1 to 1 routing between cards in Dante Controller) as your insert to the channel that you wanted to add the FX to.
Hopefully that makes sense. Using tielines does not use up any processing in the consoles (so those channels don’t need to be assigned on the board and they don’t count towards the available input count).