I know what works and I know what only appears to work, and I know how far south these things can go across that broad range. This is after 51 years experience consulting and dealing with city building departments nationally.
I was unable to call and confirm that company I gave you a link to that only did stone work that late in the day, their web site listed *complete restorations of entire buildings not just stone work.
The reason I pointed you in that direction as a step #1, are many....in summary, only those with hands on experience dealing with the city know how to avoid the endless, costly and often unnecessary hoops the city will put you through... the inspector type agencies most often do not, they are only interested in selling you a canned report for upwards of $500 to $1,000... without concerns for finding an optimal solution for you.
The report will be 10 or 20 pages with photo's... there are about 8 firms in the area that can provide that... it will be a 'fill in the blanks computer run', filled in by a person who is a generalist at best, ***** ***** out of work car salesman.
That will not be in your best interests... some will be taking a commission on any work they can sell you... the more the better.
That work, and that commission will be intended to their benefit, not yours. I can certainly steer you in that direction if you wish.
There are two dozen or more HVAC contractors in your area who will do that investigation for you as well, mostly with an eye toward selling you as large a project as possible...They will charge you $125 an hour, and take a full day doing the report.
I would like to avoid the bias, and those costs if possible, if it is OK with you.
There is no shortage of mechanical engineering or architectural firms who will be more than happy to do this for you, rates vary from $125 to $200 an hour, and their intent will be to cover their behinds and make money, not look for the most efficient way to get beyond what may, or may not be, bogus or over stated requirements by the city.
There are long lists of those in your local phone book.
I am not here to earn $10 for 2 hours work...
I am retired now, my interest for whatever reason is to provide the most optimal options for the people I work with as possible.
So far, in my view, in this case it will be best to get to the unbiased insiders in your area for what you might call 'good old boy' advice on how to proceed...
It is not nearly as clear cut as it can appear.
In way more than a few localities, entire large scale projects have been held up by a single building official for entirely doubtful reasons, and for reasons that do not look good in print...sometimes these serve jail time, but most often not.
That is why I am looking to find you the most optimal approach...an insiders route so to speak.
I will spend an unlimited amount of time on this for you if you wish.
Let me know if you would like me to continue or opt out to someone else here who can give the long list of local private home and building inspectors, mechanical contractors etc. in the area.