@Trevor Smith
I don't think you are as necessarily bad off as you think, as long as you keep moving forward and just get it done and sold. If you refinance it and rent it out there is no way it will cash flow based on what houses are renting for in Richardson, and if you lock yourself into a lease with a tenant, then you'll be losing money every month for at least the next year -- and stressed out the whole time. You could do a shorter-term lease, and then put it on the market during the prime selling season next summer, but you never know what the market will be like then. It's entirely possible with appreciation you'll have recouped everything, but it's a risk, and based on your description of what you're feeling right now, I doubt it's the type of risk you're in a position to take. This will never, ever be a cash-flowing property, and you shouldn't keep it as a long-term rental.
Keep in mind Richardson is very much in demand, and depending on which school district (elementary and JH) the house is in, some of those neighborhoods are still appreciating about .5-1% per month on average right now, subject to market conditions. That's about the equivalent of your holding costs per month. Not quite as much demand if you put it on the market for sale in winter, but you'd still be able to sell it at the right price.
You mentioned your rehab budget was $82,000, and you think you'll go over that by $15,000. That's an enormous rehab for a house in Richardson. I don't know your background or the extent of the rehab, but my guess is there are professional flippers who can do that same rehab for probably 60% of your cost. You could always just try to wholesale the house right now to someone else and get out breaking even depending on where you are in the rehab. Or just finish it up, put it on the market, and get it sold.
As you said, you could go over what went wrong with the deal, but that doesn't matter now. Just sell it and move on. Don't worry about how much money you're making compared to others. There's no general rule. I know guys who are flipping five houses a month and happy just to make $7,000 on each deal (I could never do that, but they do). Your success is based on whatever goals you set for yourself. If you lose money on the sale, well you've learned something, but at least you won't be stressed out anymore.
Good luck!
Chad
P.S. None of this is meant as financial or legal advice.