I definitely agree with this. When we went to visit Anabelle (I already knew her but my husband did not) my husband sat down on the porch at the shelter and she walked right up to him and put her head in his lap. It's like she knew he was the one taking her home.I don't have an answer to the question you're asking but I'll tell you what the wifey and I did. We went to a basset rescue and the lady has about 100 bassets. We first went in there with the intention of finding the "cutest" one". hahahahaha. The rescue lady looked at us and said "Don't even try it. One of them will pick you, not the other way around". Best advice ever. She was soooo right. Woofus was the only one to not leave our sides for 2 hrs the first time we went, and when we went back he wouldn't leave us alone. HE chose us. Great experience. Good luck in your quest
I don't see any problem with it as long as the money is going to a reputable rescue and not to the breeder (who I have to assume is a backyard breeder). You might not get a basset that perfectly meets the breed standard, but that will always be the case with puppies that don't come from an established and reputable breeder.
Puppies are always the fastest to get adopted, though, so while I would think over the decision thoroughly, keep in mind that they won't be there forever. $350 seems steep for a shelter dog, so I have to guess they know that the puppies will have some demand from potential adopters. At the shelter I am involved with, all puppies are $175.