I think you maybe have a few things to think about here - there is a lot of scope in your question.
This is very much an "Engineering" question, unlike a lot of this forum, which is more about "Science" or "Technology"- and therefore the main word is compromise.. Where do you want to compromise? That will affect all of your materials decisions.
For example - You have two different materials for Inlet and exhaust valves going into a third material of the headers, all with different coefficients of expansion. This is going to need some tuning - they will work best at certain temps and RPM ranges, and not others. Where do you want your scarfices to be? Will you give up some middle range torque for some top end RPM's?
Every time you mix two materials, you will have to make all of these choices. There is a lot of be said for using a single material throughout - for example Ti, but that also brings comprimises as well - depending on your desired outcomes it shows where the comprimises are made. When you know your comprimises you can select your materials... it has to be a "right to left" plan. Outcomes -> decisions -> comprimises -> materials.
But... if you're making a fantasy engine, why give yourself the limits that you have? A 2 stroke engine would have a lot of benefits over a 4 stroke - a lot more power per cc of capcity for one and a much higher rev range within practical engineering limits. If it only has to last race distance, why not use a Wankel engine? All the issues with them are down to trying to create longitevity - not an issue for a race distance. If you want efficiency and torque, then the Ilmoor double acting four stroke engine - they call it a "5 stroke" - has a huge amount of potential. Couple that with a CVT gearbox then you have some very.....different.... but potentially something game changing in a race powertrain.
When it comes to valve gear I agree with Lycoming. You could use Desmodronic, or any other positively closing valve gear - but what ever it is, you will be leaving a huge amount of power and flexibility on the table. From a race engine design point of view, there is nothing good about camshafts or desmo systems - they soak up a depressingly large fraction of available power, that could be going to the wheels, but more importantly they fix the timings of the valves. Pnumatics allow for entirely independent control of each valve, which brings with it a vast scope for tuning that is simply not possible with cams or gears.
Your point about Beryillium copper is interesting. I know that it's the "ideal" valve seat, but it's truely awful stuff to work with. Setting aside that it's lethally toxic to the people working it, it is also the single most awful to machine material I have ever encountered - it made me invent entire new swear words to express my rage with it. Your fabricators will be so angry having to work on it that they'll just go on strike.
Engine building is not like Aero design - more than anywhere else in a car - even painful areas like a gearbox and cooling systems- engine design is about choosing the least worst options, not the "best" options - for every element you optimise, you end up having to fight 10 new components that have been comprimised.