Hey, I sympathize with your situation. I lost my job and had to move too recently.
A couple of comments, I don't think capital gains applies if you are forced to move because of work. I checked in to that myself with several CPAs and I got the same answer every time, if you make money but you were forced to move because of work, you are okay, there is an exception for job loss.
Here is another idea, not an answer. I bought a house that I was not planning to turn into a rental, then I got laid off.
I took my own pictures of the inside and outside of my house and ran my add 6 months before I knew I was going to move. My ad was a bit fake. I used Craigslist. I priced it really high for my area and lowered it until I started to get hits for renting it. Then I knew what price I could get for it. Clean your place up real nice, stage it best you can and take pics your self, then see what you get on your ad. You might be surprised at the rent you can get.
I would not take Property Management Companies word for it on the rent amount. Just like realtors want to sell your house super cheap (often) so it sells quick for them, PM often low ball the rent they will lease it for you, it makes their job easier and means it is filled quickly. They just make the one month rent and a percentage. An extra $100-$200 bucks is change to them, but makes a big deal to you. Don't assume they care or have your best interests in mind.
Last, you won't hear many people say this on hear, but if you have at least one trusted friend in your city where your house is, you can manage your property long distance.
Get any pesky maintenance issues fixed now, before you move. Look for one friend you can trust who could be identified as a property manager, maybe even offer them a little cash for a trip here and there, and rely on them.
Here is why I say this, it sounds like you need a little time for the property to go up before you can sell. You can manage long distance for one year, if you have a friend who helps you, every once in a while. If this is your only property, you don't have other ones to worry about, you could do this.
I am currently managing a property long distance, its been fine. I have a friend who is a neighbor who lives across the street, and she can make a quick trip over if I ask her. You only have one property, it could be done.
I know this is like completely against the BP Bible, but there are landlords who self manage long distance. That is actually done, and rather than take negative cashflow, I would take that chance for a year.
Last, don't list with a realtor if you do try to sell. With Zillow and Craigslist, you can list your house on the internet without using them and losing thousands of dollars you cannot afford to lose.
It is possible to sell your house, without a realtor, this is where a good friend, who cares about you might come in handy.
You can offer to pay them a little to babysit a walk through for a potential buyer and save thousands of dollars.
I know lot of people might disagree with me on some of these suggestions, but I have done every one of them myself already, and saved thousands of dollars. Good luck, and don't beat yourself up, its a learning game and this is on the path of your learning curse. You can bounce back.