Academy P-38F Glacier Girl nose weight amount?

I use 21 grams (3/4 oz), it's enough to bring the nose back down if you set it down tail down.

Not sure of the weight necessary, but I cannot extoll the virtues enough of using tungsten putty to add weight to noses.  It is dense, and has a high mass to weight ratio.  I get mine in the Pinewood derby section of my local hobby shop/craft store.  Its also available on Amazon....

The Tamiya Lightning comes with 3 stainless ball bearings - one in the nose, and one behind each prop. They weigh 32 grams, or 1.1 ounces.
There's probably enough room in your Academy kit to fit it all in the nose.
I normally just tape all the airframe together and place the airframe on a triangular ruler about where the main gear will be and add weight until the tail refuses to sit....then add jest a titch more. Works every time.
I managed to get a coupla pounds of superfine lead shot from a previous employer in aerospace - they use it to fill weight bags to adjust and document CG points during flight testing. That stuff is sorta the bee's knees. Maximum weight for smallest volume.

Something that seems to work for me is dry fitting the major components with tape to hold it together along with a guesstimate of nose weight taped in the nose. Then sit it on your hobby knife where the rear wheels would be and see which way it wants to fall.