hold the phone
I'm a bit confused, you mention runway 25L at HKG and then talk about a RIGHT turn in the go-around procedure. The Jepp charts in front of me show a LEFT turn off 25L ("straight ahead to 7DME, then left to 165 deg") - the right turn is for the go-around off 25R.
Be that as it may, we have an "engine failure - take off and missed approach" procedure in our Jepps and off both 25L & R it involves flying runway heading to 6DME and then turning LEFT ie away from the high ground. This procedure has been approved by HKG ATC - although we are reminded by our trainers to be very vocal about reminding them that we're not following the standard go-around - and takes care of the high ground problem.
Ref your point about what happens if the engine fails during the go-around - it seems to me that the situation will not be quite as critical as all that if you have the engine out procedure that we have. Looking at the all-engines go-around off 25R, you follow the runway heading until 3DME before turning right. Given that this is the ILS DME, which reads 0 at the approach end of the runway, and also that with a DH of 220' you will commence the go-around about 1 mile short of the approach threshold, this means that you will have 6 miles or so between commencing the go-around and hitting the 3DME point and commencing the right turn. In my company, if the engine fails at any time in these 6 miles then we will not turn right at 3DME but continue to 6DME and turn left. No problem. In the worst case, if an engine fails at 3DME just after we've begun our turn to the right, then will this really be a problem? We've had 6 miles of climb on all engines - we will probably be close to 3000' already. Still a very tense situation that will call for some quick decisions, but not quite the emergency situation that you envisage.
I hope this helps.
t
(Edited for kak spelling, grammar and syntax!)