What to use for closing off cavity walls finishing at first floor height?

[ruggers]

I'm building a 2 storey house with an internal garage thats accessed internally from the utility room. the 2 external walls are 350mm insulated cavity (100/100/50/100), and the 2 internal walls to the house are 300mm full fill PIR (100/100/100) and will only go up to first floor joist level. The 300mm walls separate the garage to utility and the garage to hallway.

 

Theres a room above the garage ceiling, I'm using posi joists on masonry hangers for air tightness, but, the ends of the joists above the garage and hallway/landing are to sit on the 300mm cavity divide wall. I'm now wanting to extend this hallway/landing garage divide wall up to the first floor ceiling level so I have a solid wall up the side of the stairs. I can either do this on the house side single wall only, or continue both sides of the 300mm wall up to the roof truss level, which loses 200mm of space from the room above the garage.

 

If I continue the inner wall right up, but leave the garage side finishing at first floor height with the joists resting on the divide wall, what should I be closing off this cavity with to prevent cavity air working it's way up into my floor void? It will be 100mm PIR so shouldn't be much space for air movement, but unless closed off it's not airtight.

 

It would need to be strong enough to allow the joist ends to sit on it.