I suspect Beng knows more than most about the real Domiracer.
But for what it is worth I offer the following derived from photos, press reports (contempary and later).
The first thing I will say that nearly everything written even in the best journals is partly wrong so I fully prepared to beleive some of what I will report is myth. My interest is not from any personel experience of the Domiracer but from trying to get information for tuning my own 500 Dominator for NZ Classic racing.
I understand Norton proposed the 500 twin pushrod motor in the early 1960s as a cheap replacement for the Manx. It was lighter than the Manx engine and arguably cheaper to produce. Doug Hele was assigned the task of developing the engine. It was run in the lowboy frame. So far as I know it was run in only two World Champ events , the 1963 Senior TT and the Ulster GP. The rider in the Manx gaining third place behind two single cylinder Manx Nortons was indeed Australian Tom Phillis. (Did this machine have a 5 speed gear box???) Phil Read practiced on one and dropped it - reportedly because of the abrupt power curve. He then used a Manx in the race.
So far as what the engine specifications were you get into a very big messy bunch of stories. I remember reading a contemporary report whcih said there were at least 3 engines in the Island and none of them were the same. I have no reputable data on bore and stroke. The engines did have eccentric tappet adjustment. The heads were the basis for all the latter SS type heads which are remarkably similar all the way from the 500 SS through to the last Commando. I mean the basic casting. Details on bolt pattern and ports vary but the basic head is very similar all the way through. When Paul Dunstal got the engines he reported nothing was the same as the standard engine - but I have never seen any actual factual data from him on these motors.
Then there were the Daytona Dominators. Beng knows about them.
There is a chapter in the second edition of the Manx Norton by Mick Walker but no one is saying this is all perfectly correct either.
From my own experience of running a Norton 500 twin (standard bore and stroke) I know they will have had issues with poor power spread once they got the power up. I use very long header pipes to fix this. In the long run I think reliability would have been the issue. A race motor is just so much more easy to tune. Production based bikes are built to a price and everyone who has ever tried to race production based machines against real racing machines struggles with reliability. You can make them as fast - but not for as long.
John