I know- I did car audio for over 20 years. The point of bracing a box is to keep it from resonating. The rest is overkill. DynaMat lowers the resonant frequency, bracing raises it to a place that it won't be a problem when it's caused by low frequencies. Also, unless the surface is right, Dynamat won't stick for long. Peel N Stick would probably work better- it's made for attaching to building materials and DynaMat is made for attaching to painted metal surfaces.
Give it a shot. If you're building your own and can actually test the results, build two boxes and add a second layer of MDF to the exterior, using wood glue and screws, staples or brad nails Then, measure the response and if possible, the cabinet's resonant frequency. If you have a lot of time and materials, try building the box with two layers of MDF and a layer of vinyl between them.
There's already a lot of info about this kind of thing- google is your friend.
Both approaches of stiffening and dampening do different things.
Rigidity does raise the resonance points of the panels and make the reduction of vibration easier to control.
The Dynamat (or its equivalent) works by absorption. Actually, it converts mechanical energy into heat. Bracing does not.
Imagine an infinitely well braced cabinet (cement is a good example). You have 100% of the rear wave energy now trapped or contained in the cabinet.
Actually, no. The rear wave will return to vibrate the cone of the driver or exit the port. This is where stuffing comes in. Like Dynamat it converts the mechanical acoustic energy into heat.
The point is, bracing alone is not sufficient. Adding a layer of Dynamat will help reduce the mechanical energy along with the use of stuffing.
As far as sticking inside the cabinet, I would not give Peel & Seal much better chance than Dynamat. I have a roll of Peel & Seal that has never been used and is a few years old. The glue has deteriorated so much so that it sticks to nothing.
The Peacemaker looks interesting, too. However, Vance Dickason points out that multiple layers of 30# roofing felt has been successfully used in the industry commercially for decades.
Roofing felt is loosely stapled to the inside walls with 3 to 5 layers. It is cheap and easy to deploy with little worry of adhesion issues.
That may be a simple and inexpensive alternative to mass loaded vinyl and the other products mentioned.