I have always felt that if the Shadchan could set them both up to be hired by an agency as babysitters, it could solve a lot of problems. First of all, background checks would be required and would be done be a disinterested third party. More importantly, they are imitating a typical night at home with the kids. If the boy can see that this women would make a great mother, maybe he would be willing to overlook the fact that she isn’t the most attractive woman available. Tznius would be guaranteed by video cameras, microphones, etc.
And even if babysitting wouldn’t work, the basic idea is to make them co-workers first and gradually develop a relationship. It avoids the high-stress, high-stakes date. Because it isn’t a date at all. They don’t have to talk about anything other than the job at hand if they don’t want to. Even if you know in the first five minutes, that this person isn’t for you, it doesn’t matter. You’re being paid to do a job and this person is your co-worker.
The two of them could be set up this way without even telling either of them who their co-worker is going to be. No personal questions about the other person until you agree to be their co-worker a second time.