Understanding the complete process of abating the asbestos may help with your decision. Finding out if each company will do a complete "poly" (encapsuling the entire work area with plastic... ceiling, walls and floors), if they will dampen everything prior to removal, and whether or not they hand wash and vacuum the entire area may clarify your decision.
If the procedure is done carefully and correctly air quality contamination can be minimal......but safety should be your primary concern.
but I would expect that the Heating and Ducts have been installed more recently.
I would ask a good Heating Company to inspect and make recomendations.
The AIR is the only thing you are really worried about with respect to Asbestos.
You didn't mention any concern about LEAD, but that would be a more likely problem.
These are problems that you inherit when you mess around with a 75 year old house.
Good luck and may God bless
If I were in your shoes I would go with the contractor that guarantees 100% removal (including air). Then I would have a separate company test for air clearance. This way if asbestos is found in the air you won't take on additional cost but you will have the comfort of knowing it has been completely removed.
You might also be interested in http://www.epa.gov/asbestos/pubs/ashome.html that answers the common questions below:
What Is Asbestos?
How Can Asbestos Affect My Health?
Where Can I Find Asbestos And When Can It Be A Problem?
Examples of Where Asbestos Hazards May Be Found In The Home
What Should Be Done About Asbestos In The Home?
How To Identify Materials That Contain Asbestos
How To Manage An Asbestos Problem
Asbestos Do's And Don'ts for the Homeowner
Asbestos Professionals: Who Are They and What Can They Do?
If You Hire A Professional Asbestos Inspector
If You Hire A Corrective-Action Contractor
The main EPA asbestos page is http://www.epa.gov/asbestos/index.html
Additionally, I would ask for contractor referrals from people you know and trust. I would also vet any suggestions via the online service http://www.angieslist.com , which I personally use because it has a great customer feedback rating system.
The Company I have used several times with excellent results is http://www.benchmarkenvironmental.com/ab_contact.html - They have been around for many years and are excellent at what they do.
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