at melbourne, where Land and Hold Short Ops/LAHSO is common practice, the distance between the threshold of runway 34 and the intersection with runway 27 (ie. the point where the aircraft must hold short) is actually longer than all of runway 27. Runway 27 is long enough to land a 744, so there is plenty of room on 34 when LAHSO is in operation.
To participate in LAHSO, pilot's require specific approvals. Australian domestic carriers (QF,
VB, JST and REX) can participate, some Air New Zealand flights can also. I'm not sure if Tiger have approval or not yet.
The arrivals are timed where so that even if everything went wrong that possibly could - ie brake failures, go around etc... - all at once, the aircraft still shouldn't hit each other.
With regards to a go around/missed approach - the standard procedure is to turn both aircraft to the right. There are minimum visibility criteria that must be met for LAHSO to be approved, so the two aircraft are able to see each other.