Heathrow Director's experience is of British STARs of course! Elsewhere, they often (perhaps usually) go all the way to the Final Approach Course Fix, around 10 nm final, or to a Downwind Termination Waypoint abeam final to a specific runway.
For us, there are two basic scenarios for a runway change. The planned change occurs when the wind is light enough to allow downwind operations until traffic allows, or when we expect the wind to shift significantly and we have the opportunity to change runways in advance.
In this case, the key is to find a natural gap in the arriving traffic, such that no more than one or two aircraft will have to hold outside the CTA. Coordination with the tower should result in the right number of departures heading for the existing runway direction to fit the arrivals in or close to the CTA which will stick with the existing runway direction.
An unplanned runway change will usually occur when the wind has suddenly shifted, perhaps leading to one or two go-arounds. In this case, the first reaction is to stop more arrivals entering the CTA. The hold is the safest place for them if the CTA is already close to capacity. If there are departures which can accept the tailwind component and which are more efficiently dealt with by getting them airborne from the exisiting runway direction, the likelihood is that they will be kept fairly low while the arrivals are vectored for the other end. Other departures will either be taxied for the other end or kept on stand until the runway change is complete.
Conflictions between go-arounds and arrivals really should not occur. If the published go-around is to 3,000 ft, arrivals will be kept at or above 4,000 ft until the last arrival has landed on the original runway. Likewise, arrivals will be kept 1,000 ft or more above the altitude to which departures climb on the SID.
As HD says, there is a checklist involved so that everyone is in the loop. While a quick runway change mandated by weather can be hard work, it is not a seat-of-the-pants thing. Separation is assured not just against the traffic you currently have, but also against departures not yet airborne and against possible go-arounds.