Eagle Scout here as well, 1995.
First of all, you need to decide if the knife you are wanting to make for him will be a presentation grade knife that will sit in a display along side the display box for the Eagle medal or, a knife that will see use in a camp or covered in blood dressing a kill.
This choice will dictate what materials to use and how fancy you make it.
If he is still active in Scouting and hunts, as you mentioned, I think he would enjoy a nice user knife vs. a fancy knife that will sit in a display.
As to the fixed vs. folder question this is my opinion on it- If the current council and troop he resides in (and plans on staying active with) allows a fixed blade, by all means that is what you should go for. I look at it like this, becoming an Eagle Scout is a MAJOR step along the lines of maturity, centering on aspects of dependability, honesty, respect and devotion. I would want him to wear his new knife openly and proudly, showing that with the transition to Eagle Scout he has been given a wonderful gift and, most importantly, he is trusted enough to make proper use of the gift. I think that a folder, while still a very nice gift, will get "hidden away" to blend in. Personally, I don't like to blend in. A young man just turning Eagle and getting a super nice fixed blade knife as a gift, will want to display his gift.
Now, all that aside (btw, I had a really hard time trying to convey what I was really trying to say there without seeming like I was promoting him waving a fixed blade knife around like a madman for all to see, lol).
Design: I think a decent size hunter style would fit the bill, not too big and not too small. If you are comfortable with building the blade yourself, by all means go for that. However, if you don't think you are up to the task, there is no shame in finding a very nice blade blank and doing your customizing from there.
Couple of blade designs that I like and have made knives from:
Handle: This is where the fun begins. I can't view the picture of the eagle mosaic pin, so I can't comment on them. You could go with some nice stabilized wood. Or, make up a laminate using a piece of OD green micarta on the bottom and a piece of tan on top...signifying the BSA uniform.
Embellishments: You can try your hand at some custom filework (on blade blanks, you will need diamond files). Add some jimping to the spine. If the blade is carbon steel, do a patterned patina on the blade. For a lanyard, some red, white and blue paracord would make a fitting lanyard...maybe add to it if you could find a bead that fits the design.
Getting to the sheath: This is a whole other canvas to be used for this piece and TONS of ideas are available.