Nat' Park riding/Smoky Mt'n in Particular

Just scored June reservations. Got "good" spot, but we should have known 2 pounce the moment the 6 month reservation window opened 2 beat out the "in the know" campers 4 the trophy spots. When we went in '09 we took pedal bikes and rode the loop. A great experience. But I have room in the truck 4 both of our bikes AND for my Bikee E2 motorized tandem recumbent. I think it would be just the thing for riding up and down the steeper roads (not trails) at speeds allowing us 2 check things out.

I searched, and it looks like my bike is legal in Tennessee, and that we are legal riders. And I could NOT find any weasel words in the SMNP related web sites about excluding such bikes. These exclusions R common 4 state parks.

So, (1) has anyone seen such exclusions 4 SMNP?, (2) R there general exclusions 4 national parks?, (3) could those with specific experience putting in SMNP share with us?

@DBB Thanks, you talked me out of it. We spent 5 days there, 4 years ago, but mostly hiked and did a few things out of the park. So, either I forgot about the bad roads, or we didn't drive on many of them. Either way, I trust your judgement.