Well, I think it should be sunk into the ground (but the station itself probably needn't be actually in tunnel, it could be open-top) and have a through route to Manchester from the outset. The bypass line round the east of Birmingham would then not be needed, which would offset the additional cost slightly.
The reason this won't happen is linked to the whole way HS2 Limited are thinking about the future operation of the High Speed Line as a series of separate routes connecting dedicated city pairs.
This is very different to traditional UK railway operation so it creates a bit of "cognitive dissonance" for those of us who are used to the traditional way of doing things.
They essentially see 2 types of services operating on HS2.
The first is what we are used to - mainly classic compatible services linking a number of different towns and cities in the north to London and Birmingham and providing intermediate journey opportunities as well. These are:
2tph Liverpool - London
1tph Preston - London
1tph Newcastle - Birmingham
1tph Edinburgh / Glasgow - Birmingham
2tph Leeds - Birmingham
The second is high speed non stop 400m European gauge services linking a single high demand city pair to each other. These are:
3tph London - Birmingham
3tph London - Manchester
2tph Birmingham - Manchester
The 8tph Edinburgh / Glasgow / Newcastle / York / Leeds - London services are somewhere in between the 2 concepts.
The advantage of these high frequency non stop city pairs is to allow demand based pricing specific to the flow and therefore increase passenger occupancy significantly. Think of them as more like airline services where the aim is to have each train priced to run at around 80% occupancy for the whole journey.
Effectively you save money because you aren't carrying an empty seat from Glasgow - Birmingham that is only used for the final stretch from Birmingham - London.
If there is sufficient demand to run at least a 2tph service between each city pair (which HS2 believe there is) then no one suffers from lack of connections as each city pair has direct trains to where people want to go.
So the question is what additional services would use a through Birmingham station in either direction? Why slow down London - Manchester passengers by calling at Curzon Street when we can justify running 2-3tph dedicated non stop services between each pair of Birmingham, London, and Manchester?