I think you are correct, Jerry, that it is a Briklee. Is the action a pinned barrel or a threaded barrel? It is a scrubbed stock so can easily be replaced as blade paratrooper bayonets are very hard to find and more expensive as well. I think Larry has a Para spike bayonet and I may be able to swap you out for a scrubbed stock cut for a spike bayonet if you end up going that route. Other options, find a regular blade bayonet and grind it down to a Para length blade(still expensive), or cut the stock out for a spike bayonet slot.(if you are handy with a router, this is the cheapest option)
Spike bayonet lower ferrules have a U shaped cut out, whereas blade bayonet ferrules have a V shaped cutout. If your ferrule has a U shaped cutout then the stock you have is not correct for the action.
If your actions are both the same(pinned vs. threaded) and both stocks are scrubbed then you could try swapping stocks for yet another option.