Personally I think it's best to look at the energy systems you are using to understand what's going wrong.
First of all a really important thing to understand is that power endurance (or the anaerobic latic system) is not hugely trainable. If you do 4 to 6 weeks work in this area you'll max it out and you won't see much bigger gains. The true gains come from training endurance (aerobic system) and max strength (anaerobic alactic system).
More than likely it's your aerobic system that is letting you down as a boulder specific climber, as you don't use this as much when bouldering. It's this system which is often the limiting factor for boulderers who go sport climbing (myself included).
I've personally found doing arc training has massively helped my sport climbing. So doing around 30mins of easy climbing (do NOT get very pumped, a little is fine), about a 2 or 3 put of 10 effort. This will allow you to rest easier, de-pump faster, and not get as pumped in the first place.
You can do more power endurance type training along side this, but I'd only do short 3-4 week blocks, then change it up. Foot on campus is one of my favourite to do, as you said, and is very measurable.
I do 6 reps to failure, and rest as long as the previous rep. So if the first is 2:15, the. I rest 2:15. If the second is 1:40, then I rest 1:40, etc.
You can then plot this on a graph (reps x time) and it will give you a lactate curve. This shows you your ability to deal with getting pumped. The flatter the curve the fitter you are (better your aerobic system is). So to start you might be able to do 3mins 1st rep, but then 1:30 on the 2nd, 1min 3rd, and level off around 40 secs for the last 3. This means you are not particularly fit (it's a step curve). If it's more like 1st rep 3 mins, 2nd 2:30, 3rd 2:15, etc then it's a flatter curve and it shows good aerobic fitness.
If you want more info there's loads of good podcasts, the Eric Horst Training for climbing energy system ones are very useful, as was a recent lattice one with James Spragg.
Hope that helps!