Your best bet is to go with FHA loan, but lack of steady income is going to be your biggest issues.
Best idea is to find a rental home that has been listed for a while and offer owners a few months of security deposit in advance.
Correction request should not change your current lock. Do you have well documented paper trail for your lock request?
There are expired lists you can buy, but they are expensive. If you are looking to just buy one house, you may want to simply utilize this website and search FSBO listings.