They did a very fast reply and have basically said that they will consider my application as even when they had in their requirements that they normally accept HND's, Foundation Degrees and access courses as entry requirements DipHE's are of the same FHEQ level (5) so I could be elegible.
It seems to be I can study both qualifications at the same time if I can demonstrate I can face the workload that would entails. That shouldn't be difficult to demonstrate as I have been studying 4 modules per year with The OU and I have done it fine. Apparently I will not need to wait until I have my BSc(Hons) Computing under my belt to study another BSc in parallel.
Let's see what future brings and how this unfolds then but it's very good to see opportunities are there. It sounds like "everything is possible" for now and that makes me happy.
I would need to double check with The OU once I have claimed the DipHE (or maybe a bit before) to be 100% sure though. I don't want to lose my opportunity to be entitled to B29 as that's a high priority for me.