I have small amount of knowledge, I took EE360 Acoustics in electrical
engineering, I built a house with the interior walls sound proofed, and
I have built allot of loudspeaker enclosures.

1) Don't mount the dog house to the carriage.
Mount the carriage with some isolation from the ground, like rubber,
tires, or better still: hanging with springs.
2) Go for the layered effect. Walls within walls.
A wall made with 2x6 top plate and bottom plate, but 2x4 studs staggered
on interior and the exterior and fiber glass wall insulation filling the
interior is good, the interior and exterior are still coupled at the top
plate and bottom plate. Other walls, such as the sonex or lead, should
not be connected anywhere and have their own foundation. Stagger the
sound leakage of the top and bottom plate of one wall with the weak
spots of the other.
3) Treat the air intake passage as carefully as the exhaust muffler.
4) Get the exhaust stack up high, the further up, the less sound comes
back down, and the less you will have to breathe.

Be careful what you pray for, it can happen.