Rehabing well established crowns will definitely be a better option. If you do go with BRs suggestion of boiling water and vinegar i suspect you would want to do that early before the asparagus starts coming up. Also, chicken bedding compost would be a good top dressing as asparagus loves nitrogen!
I am excited to add more asparagus this year. I have several different stands around the farm but want to increase patch in my garden. It also grows all over in the ditches around here. The canning company used to grow it in the area many many years ago and it spread naturally. we see fern all over when walking the dogs and during the summer I see people out hunting for it everywhere! maybe if i get ambitious i may try and dig a crown or two if i can find it at the right time. That is an old non hybridized kind so it can spread itself unlike most crowns you buy now that are sterile.
There was an woman in our town who would drive along Hwy 14 and cut asparagus and then to around selling it at farmer's markets. She hasn't been around for a couple of years now, sort of got to loony to be out on her own. I think everyone in town has a story or two about that one. She kept things interesting at least.
That is how I had heard about the canning factory over your way that grew it. I notice it here and there in ditches all over the area, must be birds spread seeds about.