2 ways to do this:
#1- Simply send the mix out via any pair of outputs(but NOT the main outs). Connect the outputs of the Manley to any pair of inputs on the Apollo. Assign to a new stereo track(
pay attention to routing so you don't create a feedback loop) and record the signal.
#2-Create a 2-channel hardware insert with a matching pair of IO(IOW, inputs 7&8 paired with outputs 7&8). This happens in the IO setup>Insert tab. Add the hardware insert as you would any other insert(plugin), tweak to taste, Bounce Mix.
More thoughts:
re the Burl converter, try it and see if either sounds better(I would bet the Burl will win, but maybe not by a lot).
re adding stuff to the master track before sending it to mastering; that's traditionally NOT a good practice(because it can get in the way of what the ME wants to do). In this case, I would send 2 versions of the final; 1 with NO processing on the master and 1 WITH your processing as an example of what you are looking for(and tell the ME what you used).
Regarding delay compensation; in either scenario, it doesn't matter because the final mix doesn't need to be sample-accurate to the original tracks, and inserts on the master are not compensated for anyway.(I know you didn't ask, but someone else might be curious
)