Dan: At this point, you need legal counsel. No Realtor, except those licensed to practice law, can interpret your legal rights or write contract language that protects your interests. PLEASE do not take any advice from anyone on this site who is not an attorney.
The conditions under which you are being asked to complete this sale are pretty tough. Unless you have reserves to meet almost any amount of appraisal shortfall, you may well be so over-burdened that you will go bankrupt. It can be that serious.
As I understand the situation, (and I truly do not. In the first place, I can't see the documents and in the second, I am not licensed to practice law.) you really have no contract at this point. If you have an attorney who reviewed your contact (as opposed to only the seller taking advantage of this option,) ask him or her where you stand. Usually, ANY change demanded by an attorney is preceded by the phrase, "this contract is void but would be reinstated if..." or words to that effect. If so, you are at least not obligated to take on more than you can manage at this point.
Since there are multiple offers on the property, you are faced with a seller who wants an ironclad deal. It may be that you are not strong enough to give him, her or them that deal. On the other hand, there may be no one else who can either! Yours may still be the highest and best offer that the seller will get.
As a Realtor, I can give you advice as to negotiation and my advice, were you my client, would be to walk away from ANY deal that was going to exhaust your resources before you even went to closing. There are other houses that you can make your home, and, just as you could not afford the Rockefeller Mansion, (I recommend the tour.) you may find that you really just can't afford this one but can find something that will be a comfortable home. This one sure won't be, if the sheriff comes knocking for default.