Of course much depends on the wording of the listing contract as many will tell you. I think you should think about whether the listing agent has been a contributory cause in some way, that inspired this person to approach you with the lease option proposal. Does your agent know about this at all? She should be contacted and her advice solicited.
On my own lease option to buy listings I take a leasing fee equivalent to a months rent at the start of the lease and a regular listing for sale commission when the sale is consummated a number of months later. I am not suggesting that your agent should do it that way, I am just sharing how I do it.
On top of this, if you decide to pursue the lease option, you should contact a real estate lawyer. My advice is don't ever enter into a lease option agreement without legal advice.
It would probably be best to go along with your agent. The agent can make sure the paperwork is done properly and make sure that you are not getting into a losing situation. Lease options in this market are becoming more and more common and it may be your best bet .
If you signed the California Association of Realtors Residential Listing agreement it's under 4.A.1 and the California Association of Realtors Manufatcured Home Lisitng agreement it's under 6.A.1
If you read into A.2 you can see where Lease Options are included after expiration on people who have seen the property during the listing period. Most likely this would indicate that section 4.A.1 will include that lease option.
You might as well call your agent and find out if there is someway you can all agree on an alteration of the listing contract.
FYI...if your buyer has bad credit now, it will probably not improve much over the next two years. People in this situation will really need to want to change life style and mindset to get out of that situation....they need a personal finance epiphany.