What impedence are your subs?
Damping factor is greater than 300 @ 8ohms so according to what you say it's still 150@4ohms which is good. Just use thick cables and you should be fine (say 8awg to run to the subs).
-What is the cutoff you are going to use for your subs/woofers? 100Hz? 200Hz? 50Hz?
-What slope? 6dB 12dB 18dB 24dB???
If you have a high cutoff point (around 150Hz or higher) I think you should use the same amp on the bottom as you use on the top. So if you use Stratos up top, then use a stratos down low too (maybe stratos dual mono).
If you are crossing it over low (100Hz and lower) with a fairly steep slope (12dB or greater), you should be fine with the Behringer amp.
Of course, if you don't like it, sell it on eBay.
Behringer makes good stuff, and I think it's worth a shot. When I get around to building my GR subs, I am thinking of use this amp in conjunction with the RDES xover/EQ.
Enclosure Damping
There really are many choices but I think you should just experiment and choose what sounds best to you in that enclosure. One thing is for sure, you have a killer enclosure and resonance shouldn't be a serious issue.
I've used premixed concrete with good results as well as carpet padding, spray-on damping mix and dynamat (there are many cheaper alternatives to Dynamat and I think they are just as good for a lot less dinero).