What feedback has your 3x out prospect given? If none, can you ask your agent to solicit some? What is your traffic like vs. the other homes in the area? Is it comparable? If not, why not?
In your area with appropriate marketing they had less turnout on the open house? Or, in other areas? Was the marketing in advance?
Could you list it for sale or for rent at the same time? Could you change the sign in the front yard and the marketing on the MLS?
Does this help?
I also recommend listing the property as both for sale or for lease, but I would recommend that your agent contact the potential buyer beforehand to let them know that the house is going to be listed for lease and to gauge their level of interest. Contacting the prospect seems a wise move rather than just waiting for them to find out themselves that the house has been put up for rent.
I reread you question and see you have really asked for more than my initial answer.
You say your agent said that if you did improvements to the home and rented the home it would reduce the value. But you said you have it listed for less than what you have invested in it. I don't do your taxes but most of my landlords understand some redo after each lease can be deducted. A home standing vacant for a year before a sale gives you no deduction.
When doing the improvements don't do things that constantly have to be redone. Put in Tile or another hard surface floor rather than carpet. Have some left over for repair and store in attic.
Now if you are talking about major improvements such as roofing, siding and so on this needs to be done anyway renting or selling.
As for your interested party, if you place the home on the MLS as for sale and for rent, if their agent is on their toes and sees it they will tell them it is time to make a decision or the home will be rented.
If you do rent it, you can leave it for sale. You list it as for investor only, that the purchaser must live up to the lease. You do not have to show a home that is listed this way. YOu state that showing will only be scheduled after an accepted contract and the buyer have an auto option for viewing written into the contract.
Many of our Califorina investors that are looking for rentals in this area search for the ones that are already leased.
I hope this helps
Again, thank you all for your feedback, I appreciate your comments and suggestions.