Unless you just want to learn to re-cone speakers, I wouldn't recommend taking the DIY route. If you're thinking of doing it to save money, I wouldn't take the risk. The labor is a fairly small percentage of the cost of having it done professionally...the 'kit' (of parts) is by far the larger part of it. So if you screw up just one of your first few attempts, you will not have saved yourself anything at all. Making mistakes is a part of the learning process...I'm guessing every seasoned re-coner has made a few mistakes on the path to becoming seasoned. Add that to the fact that a pro guy will warranty his work and it seems like going that route is a no-brainer. The trick then is to find the right guy or the right place. Too involved to address in this thread.
I'm just now realizing that you're probably in the EU, and that your access to real, factory-trained re-coners may be more limited than here in the US. Still, aren't there competent people available to you? If you are in the US, I'd recommend contacting a local PA company to see who they take their re-cones to, if they don't do it in-house. But I have no idea how that would work in Europe, given the relative scarcity of JBL product.
Also, you'll probably find that genuine JBL rebuild kits are prohibitive in cost, if you can even find them, so you're going to be looking for after-market parts. I guess there are some after-market kits that are good enough, if not near-equivalents, but how do you ascertain that? The people who are likely to have valid opinions about which after-market kits are decent enough are going to be the folks who have re-coned a lot drivers.
If you're determined to do the DIY thing, I suggest you only buy one re-cone kit and try rebuilding just one of the E-series speakers. Then you can decide for yourself whether it's worth the effort without having too much invested. From what little I know about it, agedhorse is probably under-selling the difficulty of getting it right on the K-series; your probability of success with those seems unlikely. For my money, given the likelihood of success in rebuilding versus what the value of the rebuilt speaker would be, I wouldn't bother with the K's, but that's just my value judgement.
If you do indeed decide to DIY, you definitely should post an account of how it went, with pics. I'm sure there would be a lot of interest in it 'round these parts. Good luck!
Edit: AndyPanda's post #14 is also spot on.