@ Adam W
The Tesco garage at Newtown is 24 hr, but I think it's automated self-service from late evening on Saturday and during the early hours of Sunday morning. Can't think you'll get there before then, mainly because you would have also missed the control people at King's YHA (Dolgellau).
There's loads of ATMs in the centre of Newtown, so that should get you proof of passage.
If you're planning on thrashing through the ride (and judging from your performance on the BC4 - there's no reason why you couldn't), you better make sure your back pockets are well stocked, as you're unlikely to find anywhere open selling/serving food between Bedgellert and Llandrindod Wells.
As to the Aberhafesp control being open, there were people there last year from Saturday evening, so I presume (I know, that's always dangerous) there will be people there this year.