I've been meaning to join in on this thread for a while... but I guess life got in the way. Still, for what it's worth... here are my thoughts on the topic:
In terms of probability I think a incapacitated climber in the access line is not that low. A dead limb that the climber disloged unintentionally during his/ her ascent that hits them, attachment branch snapping dropping the climber a distance (ask me!) or just plain exhaustion. We should be discussing access in such situations.
Obviously the first thing to consider before proceeding is anchor point strength. And secondly whether you can see and can assess the whole length of the access line and it's integrity.
I think the same should hold true for this scenario as for any other, we try and go as far as we can with equipment we carry on our harness. Good news for some... bad for others. On the one hand because of Murphy and all that you can bet you won't have the specialist piece of equipment you need on site and because it
is a high stress situation and you don't want to go handling equipment you're not familiar with in such situations.
I think the attachment above is the most suitable for various reasons:
a) It gives you the most flexibility for manoeuvering.
b) It allows for a range of lanyard lengths of the injured climber. If they are using a short lanyard and you're counting on attaching below their attachment you're really going to struggle
c) There is not risk of attaching to the wrong part of the line
The last point is really relevant - let's assume the climber has taken a fall in to their hitch, it's going to be well cinched down. If you've choked one part of the line and plan to run the rescue off the choked part of the line, how are you going to be quite sure which one it is on a long access? You run the risk of finding out when you unload the injured climbers footlock lanyard. Or cut it... yeouch!
Attached is the way I'd run this rescue, I left out the climbers for clarity's sake . Obviously one of a range of possibilities. In the end the main point is probably finding a way that suits your style, discuss it with the crew and to practice it.