We have had one experience of placement and all worked out fine, but they are case by case and circumstances for all (renter and owner) are considered.
I do not think you will get it through with a management company. They have pretty strict requirements and they represent the home owners and it is there job to weed through the applications and find the most likely to pay. Unfortunately a prior eviction (regardless of the story or reason for it) showing up on your credit report will probably keep you out of the loop with them.
I recommend you find a landlord and explain your side of the story to them upfront without paying any application fee and see what they say.....I have known a couple of people that have done that with good success as they try to rebuild after the eviction.
Coldwell Banker United