I was told I need to get a permit from the city...??  

@Jai Sookhakitchpermitting such a thing will be your biggest challenge.. most large quaries are owned these days by national type corporations that have millions and time it takes to get these permitted. 

That said so far he's done a good job (permitting, sub contractor recommendations), and my Dad who is in highway construction thinks he'll work well.

That would be the first thing I would consider if I were in your position.I am like you, if it is work that is not requiring a permit to do, it doesn't need to be done by someone with a license.

Can anyone tell me how big of a deal it is to have work done without permits?

That means that even though the type of use is not permitted under the code the local zoning board granted a variance.

Maybe see if the Mayor will give you a 10-year permit?

Can you tell me what kind of permits you got in order for philadelphia prior to renting out?

This rental property will be held in our 401K Trust, which permits only non-recourse loans.The lender is an individual, and I'm writing the mortgage and note.  

My basic research gives me the impression they have a lot of experience, so they should be able to do design, permitting, and construction efficiently, so it is good to hear from an actual client.