I think the majority of the passengers at Overton, Whitchurch and Grateley will be travelling to and from London. The prospect of two trains an hour off-peak isn't going to make up for the peak-time journey taking half an hour longer.
In my post I specifically said that they would keep their existing peak hour services, mostly because the Basingstoke Stoppers (at least in the morning) start from beyond Basingstoke.
As I said, that would remove a lot of the unhappiness as, as you point out, it would cover most of the passengers.
Unfortunately the plans for the Manydown development do not include a new station. If there were one it would need to be in the area of Worting Junction so as to serve both the Southampton and WoE lines, and as far as I can tell from the plans the section of the development closest to the railway at that point will consist of housing. It's proposed that there should be a frequent bus service from Manydown into Basingstoke to enable rail travellers to get to the station there.
Where would the 500,000 new passengers you suggest come from? If that's the annual total of journeys, it means roughly 10,000 a week or 2,000 per day. (I'm crudely assuming they're Monday - Friday only.) 3,000 houses won't produce that number. If they did, there'd be a problem fitting them onto the trains.
Even if the station wasn't right at the centre of the development people would be willing to walk/cycle to get to a station over catching a bus to catch a train. The reason being is that it would be more reliable. However just as there's no plans currently for a station doesn't mean that one couldn't be provided at a later date. Anyway the frequent bus could just mean that people from Basingstoke between the stations then have a choice of which station to use (potentially opting for Manydown so as to be sure of a seat in the morning peak)
I'm not sure that a station would have to serve both lines, infact due to the cost of building a station which did it almost certainly wouldn't, as although doing so would attract more passengers the disadvantage of having to change at Basingstoke to go on the other line wouldn't be that great to justify the extra cost. Even if the station was between Oakley and the development and only served the WofE Line there would be a fair amount of people willing to use it, especially if it were well connected by cycle routes.
Given that the Manydown Masterplan document highlights that area is mostly under the ownership of HCC/BDBC there's little stopping them from building a station anywhere in that area.
Why wouldn't 3,000 homes produce 500,000 passengers a year? 3,000 homes is likely to be circa 7,200 people, add in the circa 5,300 from Oakley and you're not that different from the population of Hook and Odiham. Then look at Hook station which has circa 800,000 passengers a year. Now whilst that would reduce rail usage at Basingstoke a little, probably not all that much.
Alternatively Whitchurch had a population of circa 7,200, with few other settlements of note nearby, and produces 300,000 passengers a year. As such, even if I'm over estimating I'd suggest not by very much (especially with Oakley and parts off Basingstoke being so close).
2,000 passengers a day over a 15 hour day is likely to be up to 200 passengers an hour, however that's a two way flow and counts arrivals and departures so on any one train at any given time, even assuming 1tph, it's likely to be at most 150. With 2tph and allowing for some weekend traveling that's likely to fall to a maximum of 70 per train (mostly closer to the 20-30 range). That's about 1 coaches worth on peak hour trains which are likely to be at least 8 coaches long. I suspect that hardly going to cause significant problems. Especially given that there's the potential for several of those to change trains to other destinations (such as Reading).