Why would you want to mix ASP.Net and PHP? You could do this all in PHP or vice versa.
Are you planning to use PHP4Mono? And if so, I doubt HelioHost would be suitable.
And as a side note, I think it would be best to build a core application server that handles calculations on a multithreaded pipeline basis. That's, of course, if your game uses some streamlined mechanics as in OGame.
But of course that would require some sort of a dedicated server, in which case the technical requirements render any (whether free or not) shared web host unusable. So, you're stuck with the scripting language itself, and this will cause a performance penalty. Maybe the penalty can be avoided partially, by using stored procedures in a PostgreSQL database and storing preemptive results; but it has to be designed carefully.
Anyway...
I know it seems like a basic task to design and build such a game, and to an extent it is, but it's still a huge load to carry on just two shoulders.
Wish you luck..