The structural foam molding process using N2 is mostly for the manufacture of large structural parts (think of plastic pallets) with density reductions of 5-20%. Wall thickness is typically .180″- .375″ with some cross section where ribs or bosses come together around .5″. Over that thickness, cycle time becomes horribly long resulting in high part costs, and tooling for a large part could cost +$100K.
Expanded PP can produced thick light weight parts, although they can be expensive compared to Expanded PS. Perhaps you are considering the PP for use because to higher heat performance.
Even though N2 is green, for PP N2 assisted foaming is not the most cost efficient process. Nitrogen has too low solubility in PP. So much higher pressure is required to get consistent foam. Maintaining high melt pressure in PP is not easy. Higher pressure means also higher cost. At lab scale – all of these looks dandy. Proof is in producing at commercial scale.
Part you are considering is too large to use a typical structural foam injection molding process. Structural foam injection molding process can never achieve low densities of EPP. For large part (even much smaller than what is discussed here), Treacle process is not suitable.
You can consider making extruded foam sheets of 1 ” thickness or 1/2″ rods using high melt strength PP and PBAs (not difficult to do – such as CO2 or i-pentane and butane. You can achieve very low densities (3 PCF – close to EPP). Than crush or cut these foam and use machine cut beads to fill cavity in your large part.
One of my clients produces PP and TPO foams with densities as low as 1.8 pounds per cubic foot (56 for solid PP) at thickness up to .500″ @ 78″ wide in rollstock form. We also laminate these products into boards or planks for fabrication, up to 1.5″, which can in turn be laminated again. If you are just looking to fill space in the plastic parts, perhaps this may make a good, thermally stable material. We may be able to fabricate particular shapes depending on you requirements.