You can only strip 2nd mortgages that have absolutely no equity. Therefore, if you only have one mortgage, you can not strip the mortgage with a Chapter 13. A deed in lieu will only satisfy the first mortgage and the second mortgage (assuming you have one) can still sue on the note. If you are underwater on the first mortgage, a deed in lieu will be difficult to obtain. Good luck!
If you don't plan on keeping the property, why go through the extra expense to lien strip?
And if you want to stay in the property as long as possible, why sign over title to your mortgage company? It just gives them the right to evict you that much sooner.
If your plan provided for paying arrearages on your mortgage, you will certainly want to see your attorney to modify your plan to omit making these payments in the future.
I would recommend speaking with your attorney before making any decisions, because your ideas won't accomplish the objectives you specify.