I've never heard that they've discounted, required more references, or excluded them simply because you haven't known them more than the required 2 years. In fact, I'm pretty sure they can't do that.
If you have folks you've known for 3-4 years and you are sure they'll give you a good reference if contacted, then use them. They MUST live in the same county as you in Delaware! NO relatives are allowed. Not by blood or marriage!
As for your friends having a criminal record... well.. unless it's something that happened recently, how else would you know? People do brilliant things -- sometimes illegal brilliant things -- and then they magically pull their head out of their rear and live out their lives as upstanding citizens. Unless you ask, you'd never know... even then, I don't know you'd get a straight answer. Who owns up to something like a criminal record?!
Best of luck to you. Don't overthink this! In my opinion, the AG's office wants proof that there are 5 folks who have known you well enough for 2 years or more that are willing to say yes, he/she isn't crazy and I think would be responsible while carrying a concealed firearm.
Moosie