It seems likely that you would be able to submit a competitive application. You know best, but it sounds like you fancy your chances in a PPE interview too. However, your first concern is asking yourself why you want a BA in PPE. Oxford will want to know too. Why not a masters? Why not another subject? And why Oxford in particular? I'm not saying you shouldn't apply - obviously. Simply, they're things you need to be absolutely clear about, especially since you're a mature student, from the very beginning.
I can't comment on your GPA scores since I'm not familiar with the system. Tutors, however, would probably care more about your aptitude in PPE than in Software Engineering. Still, if it's a very low mark, you need to be able to demonstrate commitment to your studies.
I hope some of that helps in one way or another.