I've found that at least some E2000 16 hp Greenfields have approximately the same drive system as other Greenfields: mechanical drive based on large forward and reverse clutches driven by a single V-belt that goes through a right angle by use of skew pulleys. That means that if the engine keeps running when the mower stops, either the drive belt or the clutch is slipping. I'm guessing the pictures in these two threads should be much the same as on your mower:

https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=20076&page=1

https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=21336&page=1

Can you confirm that your drive is like this one, please. If it is, we need to know whether your drive belt (the one from the crankshaft pulley to the two big clutches) is touching the bottom of the groove in the crankshaft pulley. If it is bottoming, it will slip and cause loss of drive, especially after warm-up. If it has that layout but the belt is not bottoming, it is possible that something is wrong with the pair of drive clutches. We can probably help you sort that out if that is the problem.

Please let us know the answers, and send pictures of the underside of the V belt - we may be able to tell if it has been slipping.