3 years for an FHA guaranteed loan is correct. You can get a conventional loan after 2 years however you will need 20% down.
There are a good number of investors that will do a lease purchase option. Where you are "leasing" for 1-2 years with the option to purchase at a predetermined price. In most all cases they will ask that you put some money "down" to purchase the "option". Anywhere from $1,000 to $10,000+ depending on the purchase price. There are more details and terms to be hammered out in this type of transaction however those are the basics.
Another option you may be able to explore is to have a lawyer clean your credit score. There are various services out there that will claim to "clean" your score however the most thorough that guarantee to remove all blemishes will be actual lawyers. Their fees seem to range from $1,500 to $2,500 depending how much there is to improve.
Hope this helps. If you have any other questions feel free to ask.
Best Wishes, Bryan