Hi Al
Here is my ideas and it is not just ideas it also works, as we have done quite a few builds like it and also done some consultant jobs and helped others out.
We do sell motorcycle dynos from Dynojet, that the reason why I know about this stuff, and believe me Bike engines do make a lot off noise, our construction makes it possible to use our Dynoroom 24hours and it is placed in the middle off a small village
There is two things; you have to dampen the sound inside the room and stop any sound from escaping the room.
We do it by making two rooms inside the exsisting room.
We are making use off the Rock wool stuff that is normally used under your concrete floor, it is put up in a frame system made off 1"x2" wood it is made as a room inside the room not touching the outer wall, when it is finished it is sprayed with some stuff so that the Rockwool doesn't fluff.
The outer wall is made as a wooden construction off 2"x4" ( I just love that the Fraze " and this is a 2x4, but I cant remember where it is from) that construction is then covered with 1/2" plasterboard and every seem is sealed with acrylic something I don not know the English word for.
In the wood construction is also 4" thick soft Rock wool.And again this room does not touch the outer wall.
The important thing to think about the sound as if it was water you wanted to keep in

have you ever noticed how Much noise that escapes a keyhole
This translated to a cheap DIY system would be; seal the outer wall completely every little crack needs attention.
Then a wooden construction made off 1,5"x2,25" if you that size in your shop's and then 2" Rock wool in between and plaster board everything sealed-.
Then you track dawn all the old carpet you can and you hang it dawn from the sealing about 2" from the walls but there is a risk off fire with the carpet it could be sprayed with the same stuff as is being used in theater's for the decorations.
It sound like a lot off work but a thing that is also gained is the fact that it will be lot easier to heat the workshop.
Regards
Ole.