After scrounging for parts, and opening up the box, I have modified my proposal to the following:
Note that the freq multiplier is supposed to take, at maximum, 15 dBm. The reason I put the 5 dB attenuator, then an amplifier, then another attenuator is that I don't know of / can't find easily a 10 dB amplifier with the usual case type on the MiniCircuits site. (If anyone knows of one off the top of their head, that would be handy. Then I'd remove the attenuator between the multiplier and the amplifier, and make the 10 dB attenuator a 5 dB.)
Anyhow, the ZFL-500HLN can only output 16 dBm of power, and I don't think I have space for another ZHL-2 (which can output up to 26 dBm) inside the box, so I put an attenuator before, as well as after, the amplifier.
I think I have space inside the box for all the bits and pieces I'll need, although to do things correctly, I need to drill holes in the teflon mounting plate to mount the amplifier and splitter.
I also think that I have space on the front panel to put another isolated SMA feedthrough.
I have, on my desk, all the parts (except for mounting screws, and cables between things) to make these modifications to the distribution box.