@Susan Pompea I can totally understand that you are gun shy after evicting someone who has wrecked your place. I went through this myself in July and my house is still vacant - took me 6 weeks to get the house back in order, and then we decided to take care of some other improvements that we didn't do before the last tenant. I have been trying different things over the last 6 weeks to get the vacancy filled but so far no dice.
1. you could ask for tax returns to verify the self employment income - also does he own his own shop, does he work out of his current homes garage? This would be important info to know
2. If you don't want to rent it for less - don't do it. Some people just want to see if they can save some money. If they really want it they will pay what you are asking.
3. Some people are just cheap - and some people just lie about their income. Won't know until you do the check.
4.If this is true then you shouldn't have any problem finding tenants at your asking rate.
5.If you haven't even started advertising and are getting great response, why lower the rent right now? Sounds like you have a nice house in a nice neighborhood that will rent well.
And to your last point...even the most thorough screening will not root out 100% of problem people but it sure helps. As you have learned always run all the checks, i.e. criminal, credit, rental references, employment/income, social media, etc.
Don't be afraid to deny someone when something doesn't look right. I have denied every applicant so far. I would rather have the property set empty for a little while longer than put a problem tenant in there that will cost me a lot more in the long run.
For this particular couple, my answer to the lower rent would be "I'm sorry but the rent is firm @ $$ and the longest lease I will do at this time is x months. If you would like to be considered these are the things I need from you" I also agree that someone that wants to move in 11 days could be trouble - or maybe they just are last minute people. Who knows what makes some people tick?