There are some fine pro mids that will work fine to 140-150Hz. I recommend scratching the one you were going to use, because this will be a huge factor in sound quality.
This will be easiest, and lowest weight, if you do this(and use the mid that can be crossed low): Build the cabinet in two parts and have the connect with a very soft/compliant material via a joint. A latex foam sheet is ideal and I can specify source for this material cut to specification. The woofer section and mid-range section must be decoupled. This is because the large woofer section is acting as a huge surface area to transmit mid-range band vibrations. You will build the mid-range/treble module with double walls; exterior layer then adhere in Dynamat or similar material to the inside. Clean the aluminum side of Dynamat, wipe down with solvent to clean it, and use a polyurethane adhesive to attach an inner wall/second sub cabinet inside. This will create two stiff layers with a damping core between then, resulting in massive conversion of vibration to thermal energy, by way of this trapped damping layer, in an effective shearing point between the two stiff walls. Still use lots of internal bracing; much more than you show in your picture. For the woofer module, use 3x the bracing you currently show, being sure braces attach to the walls with points no more than 5" from each other. This will ensure that the lower module has a 1st resonance point over 200Hz, well past the crossover point/band the woofer will operate. So, the woofer will effective operate in an inert cabinet, and since the mid-module is seperated via a soft layer that acts as a de-coupler, the mid-range frequencies can not transmit to the woofer section and excite it's walls. BTW, B&C is a superb driver manufacturer, and they have at least 2 mids that can be used down to 150Hz with no compromise.
My suggestions are meant to result in a cabinet that will not produce any coloration that is audible. This is a critical feature if you intend to have a reference-grade system for music reproduction.
-Chris