I think the biggest difficulty with your goal is that reasonably priced sealed subs will struggle to produce 16 Hz output with extremely low distortion
. There are plenty with MAX BURST in that range, but not sure if you would be happy with 20 or 30% distortion. I am assuming that you don't want to hear lots of 2nd and 3rd order harmonic distortion when playing 16Hz notes, and many sealed subs are going to have very high harmonic distortion below 20 Hz when attempting to produce a reasonable SPL. You can check the charts on data-bass on several sealed subs such as the SB12-NSD, and see that distortion below 20 Hz tends to be quite high.
Perhaps the Rythmik F12 would play 16 Hz at your preferred volume with very low distortion, but it is hard to say for sure as I have not found definitive output data with distortion measurements.
I think you are on the right track with dual subs....you will gain 6 dB of headroom which should assist with playing nice and clean at the level you need. More importantly, it will allow you to eq a smooth, flat response for the best quality bass possible.
I would be tempted to go with something like the Funk Audio 18.0C, but it will approach the budget that you have set for both subs. The large 18" driver should be able to produce 90 dB at 16 Hz in room with very low distortion. It produces 93 dB in outdoor ground plane testing with reasonably low distortion, so with room gain, it should play very clean at 90 dB. It is MUCH harder for a sealed 12" to produce low distortion 16 Hz output.
So although I am a HUGE fan of dual subs due to the smooth overall frequency response you can get, I think a larger driver should strongly be considered in order to get clean, distortion free 16 Hz output. Small drivers just require too much excursion to keep distortion low at that frequency.
This may not be the solution, but it may be, and I wanted to offer another perspective.