A lot of the stabilizing in a hand built wheel comes from the stress relieving done during the tensioning and trueing process. This stress relieving is actually a bit of a misnomer since it really is about stressing the spokes to encourage them to bed into the rims and hubs and to each other so they are well formed through the middle at the cross over points and better grounded at the hubs and rim. This process is something that gets missed in a machine built wheel. So with such wheels it is left to your natural riding to perform this rather important function. It also means that it's not uncommon to have to keep chasing the tensioning and trueing through multiple tuneups of the wheels before they settle in and stabilizer. Both ways are valid but most of us would rather do it once and avoid the frequent process of retrueing.

So if you can find a good wheel builder somewhere around the area and ask them for a full tuning they could go around and match the tensions more closely as they also true or align the rims and perform a couple of stress relievings on the wheel along the way. The final product you get back after this would actually be better than yet another set of machine built wheels that cost more than your current wheels just due to this stress relieving and more finely tuned tensioning and trueing.