Your LLC, I'm assuming, is a single pass-through entity that holds your real estate investments entirely....basically each property you've purchased isn't its own LLC?
That alone is going to subject your other investments you do not walk away from to the liability of the one you're looking to get out from under (which, personally, I don't think you should try to do).
Add to that, it won't just be your credit score that is affected....if the home is foreclosed and then sold at auction, you'll be responsible for any short-fall anyway - so you've not eliminated your indebtedness, just continued it, now without any property attached to the debt.
Add to that, the lender can also then place liens on your other property for the difference, take you to court for the difference, win a judgement that will stay with you until its paid upon the sale of one or more properties, or when you die and your heirs liquidate your estate.
One more add to that - the lender can also cut you a 1099, which creates a whole 'nother headache for you tax wise.
I'm not a lawyer, nor do I play one on TV, but I'd strongly suggest you make an appointment with an attorney, discuss your options and see if there is a way you can do some creative financing to keep the property and pay your debt you took responsibility for.
Perhaps you can offer the house in a rent-to-own option?
Perhaps you can refinance it and extend your payments out again so if you've paid off some of the loan (say five years) you can refinance it for thirty again, thus lowering your payment obligation each month?
Perhaps you can find a company in the area in need of an executive home and furnish it so they can rent it?
I don't know where it's located, but if it's a tourist spot, you might consider renting it out by the week or month to tourists? If it's a college town, maybe rent each bedroom seperately to students?
If all else fails, perhaps just keep paying your obligation from the positive cash-flow on your other properties?