Since it has been verified that the barrels are Parker and original to this gun, does the standard barrel design allow for either a splinter forend or a beaver tail forend?

Depends on which style of forend lug you have. The reinforced (one-piece) lug was designed for the beavertail or trap forend. But the non-reinforced style can be used with a beavertail but they have been known to pull off the barrels under heavy use.





.

Parker GHE vintage 1937
 

Would a photo of the lug assist you in determining if the barrels were originally configured to accommodate a beaver tail forearm?

Yes Charlie.

Yours has the one-piece reinforced lug.
It became standard practice at Remington to use this style of lug on all Parkers they produced regardless of the style of forend to be used.




.