I will tell you what the rules are, and you can make up your own mind what is the best way forward for you.
1. For postal applications, the day of posting is the date of application. You must send it via recorded delivery and must keep the receipt safe until you get the status.
2. For PEO applications, the date you actually attend the PEO to submit the application is the date of application. When you book the appointment is irrelevant. If you do not get an appointment before your visa expires, then it is your full responsibility to send the application by post. UKBA is under no obligation if someones visa runs out because they could not apply due to lack of appointment. Or you can say, same day PEO applications are a facility provided by UKBA, not an obligation.
regards