I THINK you can buy the new TRD logo separately and install it on your 2016 skid plate. It uses something like a half dozen holes to hold it in. At least that's how the TRD skid plate was for my 2018. IIRC the same skid plate fits all third generation trucks.
I bought mine for cheap from someone that insisted it didn't fit his truck. He had a 2018, just like mine. The skid plate fit my truck fine.
Sometimes a Toyota dealer offers % off coupons for parts bought at the dealer. Shipping is free to the dealer, saving you money. Shipping on the skid plate is the killer because of size and weight.