Howdy,
I don't know about the 37mm stuff but back in the "Day" I had a Load Bearing Vest that was designed to carry the 40mm grenades. It was standard GI stuff that was part of the old ALICE web gear system.
I never really liked it because it placed 12 40mm grenades on my chest/abdominal area. I prefer a bag that I carried either cross body under weak side arm or weak side shoulder carry to the vest.
Someone, Cobray maybe or one of the other spinoffs in Georgia, used to make one similar to the shotgun set ups.
HTH
Paul