I would suggest that you only initially lodge Form P85 asap and await HMRC's response. This is usually sufficient.
A residence determination will not, as such, be made by HMRC as this is for the taxpayer to determine and in due course if necessary the "Residence etc" Supplementary Pages of the tax return are completed. No need to distinguish between the 2011-2012 and 2012-2013 as you indicate (the P85 deals with it).
For info" the notes on the Form state:
Use this form to claim tax relief or a repayment of tax if: • you have lived or worked in the UK • you are leaving the UK, and • you may not be coming back or you don’t know when
you’re coming back or, • you are leaving the UK to work full-time abroad for at least
a complete tax year.
Do not fill this form in if: • you normally live in the UK and are going abroad for
short periods, for example on holiday or a business trip • you have completed, or are required to complete a
Self Assessment tax return for the tax year that you leave the UK (unless you are leaving the UK to work full-time abroad for at least a complete tax year for a UK based employer).
No necessity to file P50.