Advice on retroactive permits and building codes

My partner and I are first time home owners, and very happy to be moving to Dormont soon, but starting to freak out about some structural surprises in the house and wondered if anyone here would have some advice.

Going in, the 1st floor ceiling was in need of reinforcement. Our initial home inspection expected this to be a minor repair (sister some joists). After opening it up, our contractors determined it would need a new beam instead of any simpler repairs. We brought in a structural engineer for a new report, and everyone agreed that a new beam on the 1st floor ceiling was fine. It was brought up that the basement ceiling joists were also overspanned, but that the 1st floor ceiling work could proceed fine without any required basement work.

After work was completed, the inspector for some unrelated electrical work turned out to also be the borough's building inspector, and surprised us by saying we needed a permit for this structural work we and the contractors were unaware of. This was reported to the borough and we are now in the process of getting a retroactive permit. Our initial application was denied on the basis of wanting more evaluation on the overspanned basement joists.

Now when discussing with the structural engineer, they are unwilling to investigate if the overspanned basement joists are reasonably safe as-is. They are recommending we add a beam under the microscope of the building code inspector. It seems we are in a position to either pay a lot of money for an unexpected basement beam, or somehow get a structural report that satisfies the permit requirements with the understanding that the basement joists are fine as-is, as was made by everyone before.

Our best guess for next steps is shop around to different engineers or maybe explore quotes on a new beam, but cost is becoming a big factor for us. Is there anyone we should talk to?