If i remember correctly, CR9E are right for standard plugs, and CR8EIX are correct for Iridium ones, but they both cover our temperature range in this country so it's no big deal anyway. I've had CR8EIX in my bike for ages now.
These carbs do very much appreciate a carb balance, and the difference can be quite huge once levelled, but as already pointed out everything else needs to be functioning correctly first otherwise the carbs will give off a false reading and you can make the bike run even worse.
Avoid jet washing the bike, water can get in very unwanted places plus there is a high risk of blasting the engine paint off, and it comes off much easier than you would imagine, as i found out before respraying my own engine. Plus my airhorn sounded like a strangled cat once for about 3 days because of water intake.
I've found over time that hesitation or running ropey under 3000rpm can be one or even all of 3 things.
Firstly if your air filter is old and blocked then the bike simply can't breathe. No real explanation needed, if it's gagging for air then it's gonna run badly, especially at lower revs, at higher revs it'll be trying to force air through so it will feel marginally better but certainly not right. Judging by the fact you say the old plugs were very ropey then there's a good chance the filter has been overlooked as well. If you're gonna change it i would personally buy a K&N air filter you can clean and re-use, rather than a paper disposable one.
You need to do a quick TPS check on your bike to see if that is positioned correctly for starters. I recently bought my 4th unit, which was brand new so i shouldn't have any more problems now, but before that i'd bought 2 used units which lasted me for a while. The thing is i got to learn the bikes behaviour when they were slowly breaking down.
When out of the correct position the bike would run with what i can only descrive as a shivering effect, it was very mild but you could certainly hear and feel it.
When the TPS goes wrong the bike just doesn't run right at all under 3000rpm, and can become very jerky and slightly unpredictable in traffic, resulting in a lot more clutch and throttle usage.
The 3rd reason would actually be the carbs out of balance BUT you can't even think of attempting to sort that one out without the air filter and TPS being in good shape to begin with so that would be last on the list.
There is also the good chance that they could all need doing, which collectively could make the bike run like shite anyway.
I'm gonna hazard a guess that your coolant system is also clogged up. Even though you've changed the coolant, and there has certainly been warm weather, it's extremely rare for the fans to kick in on these bikes. Some people on here have never even heard theirs work before!
I would suggest buying some Radflush from Halfords and give it a proper descaling. Just stick in a bottle of it, mixed with clean tap water only, then take the bike for a 10-20 mile spin, preferably not in traffic, as you want it to circulate and descale whilst getting the effects of air cooling at the same time.
Don't go nuts on it though otherwise the plain tap water will boil in your engine like a kettle in this weather.
Then flush it all out with a hose and put some decent coolant back in. I personally prefer the ready mixed motorcycle coolant, others will mix their own, that's entirely up to you though.
Once the system is all flushed out the bike won't get so hot, your fan will probably hardly ever come on, and you'll very rarely need to even top up the coolant.
Once the bike has cooled down after a run the fluid will get sucked back into the engine from the expansion tank. If everything is working well then the coolant level in the expansion tank will remain roughly the same each time.
If the waterways are blocked the coolant can't work its way around the system well enough, so it will then start to overheat and eventually boil in the expansion tank then overflow via a pipe onto the floor.
Obviously if you check the expansion tank has a lower than normal level, or is even empty, then you know that you have issues, which will either be a clogged system, or an air leak which would normally be a loose jubilee clip at the thermostat end.
So just by checking the expansion tank level every once in a while on the centre stand, the level will tell you if your bikes cooling system is all good or not.
I don't know what spark plug caps you have on your bike but i'm gonna hazard another guess and say they're the OEM ones, which are unfortunately about £200+ a set to replace new.
Luckily we have found a perfect replacement NGK set for a fraction of the cost, which a lot of us use, including myself, and they work just fine.
Because of how cheap they are i would definitely recommend you buy a set as the OEM ones do break down as well over time.
http://www.ebay.co.uk/itm/4x-NGK-Resistor-Spark-Plug-Cap-SD05F-black-8022-/231159766652?hash=item35d2321e7c:g:lRUAAOxyOalTbQFeHope this helps.
Before you ask what a TPS is, here you go.
http://foc-u.co.uk/index.php/topic,13864.25.html