Only briefly and err.. wasn't really strong enough to do a rep

... but regardless, could not sufficently heavy leg curls work for the second part of the movement, and the first part is just a back extension right?
There's two ways of doing it: with or without back extension.
When we did it, it was without back extension. You use your knees as a fulcrum then drop down to parallel then pull yourself back up with your hammies. You have to keep the hips completely locked (ie extended) so it also trains your glutes, albeit isometrically. When it gets hard the hips want to unlock so you can use your back to help, but thats not the idea.
The difference with a leg curl is it only involves knee flexion - the hip is anchored. Hamstrings not only flex the knee, they extend the hip. With the GHR, both functions of the hamstring are being trained.
There have been a number of EMG studies done and GHR is pretty much unparalleled when it comes to hamstring activation. SLDLs and GMs are right up there as well though. The problem with SLDLs and GMs is that they load up your back too.
Glute-ham is a pretty bad name though, because glute activation on a GHR is pretty low on the scale - they only act as stabilisers and only if you are strict and keep your hips locked. Even body weight bird dogs, glute bridges, hip thrusts are harder on your glutes than GHR. GHR is really a hamstring exercise.
So, if you really want an accessory exercise for the hamstrings, GHR is great if you have the luxury of space and money. They are very very humbling. But that said, weighted GMs do an excellent job too, particularly if you use a very close stance, keep a hard arch and sit right back. You can also use bands (from under your feet to around your neck) to increase the difficulty for the hamstrings. Band or kettlebell pull throughs are another alternative that are easier on the back.
If you want a glute exercise, don't do GHRs, do barbell hip thrusts with or without bands.