fascinating to read about different experiences on here. as others have said get independent legal advice about this before proceeding. would also get your property valued to be clear about its value. then you can make informed decisions about selling on your terms.
personally can see little benefit to restricting offers to this 1 buyer, unless they will give you a premium price for the exclusive right to buy.
it could work in your favour but protect yourself with all the facts first and do have legal advice. good luck. wonder how common this cold calling with promises is?