You don't have to sign a contract to have a contract.
Electronic contracts have been well recognized in court for years.
That she wrote "consider this signed" gives it all the strength (in my opinion) of a written signed contract.
That she accepted rent under that agreement is "performance" and gives added strength to the terms of the contract.
I suggest that it would be worth your while to spend a few hundred to have a lawyer write you up a written opinion about the validity of your contract, providing statutory and case citations, that you can send to your landlord and give to any prospective buyer that comes to look at the house so that you make sure that the prospective buyer knows that you will hold them to the lease and that you have a lawyer that you are obviously willing to use.