A brief update:
I was near The Malverns yesterday so I had a quick recce.
The carpark at North Quarry is reasonably easy to find (grid ref above) and the charge is £3 for all-day parking. It's not big but there should be adequate space at 9am on a Sunday.
The snack kiosk at British Camp (about half-way along the hills) is open every weekend. As well as bacon butties, tea and coffee etc, they sell home-made rock cakes - I've tried them and they are delicious! But, the owner says, they sell out quickly. She gave me contact details and suggested that I let her know how many people would like a rock cake midway along the walk and she will keep that number of cakes aside for us 
As to walking options, the highest (and, arguably, best) section of the hills is the north end from North Hill to British Camp. This is a four mile section and includes the majority of ascent / descent. The other section is a further four miles south from British Camp to Chase End Hill.
The three most obvious options are: walk from North Hill to British Camp and back; walk from North Hill to Chase End then return in one of the cars we'll have left there earlier in the day; and, for t'hard bastards, walk from North Hill to Chase End then walk the return (perhaps avoiding some of the ascent by using low-level paths on the way back).