Sign a lease dated for one month but move in the next month

[Bryan N.]

Got an email on a rental today.  Which made my wife and I start to discuss what's the right and fair way to handle this if they pass the application process.  No app yet, just want to bounce this off others so I am prepared when I show the property on Thursday.  I have no exact details yet, but will have more Thursday when I hear the story.  This property is in the middle of a rehab and won't be ready for 2 more weeks.

2 applicants "roommates" with a current lease that ends February 5th.  One roommate is in the military and needs to be on the lease dated January 5th, because he/she is departing the country prior to February.  The other roommate is not leaving.  

So, if they apply and are approved do you:

1) Take a payment which converts into the security deposit (one months rent) to remove the property from advertising with a disclaimer that if they don't occupy by the 5th of February it is forfeited.  Technically they could start moving in January 5th since they need the lease dated that day.  That would give them 26 free days.  So, I would hold the keys under a seperate signed agreement detailing this until February.  Then February would be prorated.  

2) Charge them the security deposit and prorated amount for January since the property could possibly be rented by another applicant for January. Sign the lease and hand over the keys.  Let them move in when they feel like it.  

It's slow due to the time of year, I'm charging a premium for the property, and I can afford to pay the mortgage and utilites while its vacant.