TOPIC:

I think your problem lies with the oiled filter. An oiled filter let's very very little air through it. Hence the issue presenting at the time it needs most air. Side wind is a fallacy, it'll make no difference to performance carburation wise. Remove all the tape, all your doing is restricting air volume even further than the oiled element will allow which I believe is insufficient any way.
If you do the maths of carb size/air volume versus cubic capacity against all the z range the 650 vm24's are the most free flowing which is why they have the highest bhp v cubic capacity. 
They love loads of air and fuel but in the correct ratio's. 

Oh shit... Didn't think about that, rookie mistake I guess.

On the other hand I just finished mounting the 102,5 mains like 2 minutes ago   I managed to switch them out with the everything still attached to the bike (Won't recommend it, was a p.i.t.a, but I dont want to put more stress on the rubber boots than necessary)

I have some "not-oiled" foam laying around which is a lot thinner aswell

I'll do a test drive in the manner you mentioned with how it is right now, and if it still boggs down, I'll first try changing the filter foam, and if the problem still persists I will open the carbs AgAiN and mount the 107,5 mains. 

Thanks for taking time helping a rookie out, I really appreciate it!

To get the best out of any engine it needs to be able to breath, drink and fart as much as it wants. 

Haha, well said!

Took a small trip (about 4-5km total) with:

~ 102,5 mains
~ 15 pilot
~ Needle on 4'th notch from top
~ Oiled filter still in the airbox
~ Air screws about 1,875 turns out 

DAY AND NIGHT DIFFERENCE! It now runs good on full throttle, maybe a few spits here and there, but nothing noticeable. Probably just needs a little adjustment on the air-screws. 

However, I dont know how these bikes run stock, so in the future I might switch out the filter with a more breatheable one and up the main jet to 105/107,5

Thanks for the help!

Plugs after the little ride (cleaned and sanded them just a little bit before going out)



Should probably be more brownish, but this was just a small test ride.

do you think its gonna do any damage riding it like this if the filter "chokes" her a little?
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Running a little rich won't damage it as such, better than running weak as this would make it run hot

That is still lean but unless you do a plug read as per my previous post you'll only see what was happening just before you turned off. If you Rode flat out then stopped with the engine still running for 10 seconds on tickover the plug colour will show the tickover mixture. That's why you need to check the plug colour at high throttle openings to see what's happening at that time.
Pilot jet solely controls 0-1/3, main jet 1/3 - 3/4, and needle jet 3/4 - full throttle. 
However each overlaps the prior and post to ensure smooth transition. 
Also the pilot is operating from 0-full throttle. Ie all the time. 
To fully understand what your carbs are doing you need to do a plug colour read for each jet zone. Once you know that you can dial them perfectly. 

With regard to potential damage from a lean mixture. The leaner it is the hotter it'll run. Hotter it runs the less effective the lubrication system and higher the friction of all the touching components. 
Your better running slightly rich than lean. 

Allright! Right now I've been at it for almost 2 days straight to get it running properly, so I'm closing in, but need a break.

I'll do a plug read as soon as the sun is back, been raining for almost 2 weeks straight here now, and I'm tired of cleaning the bike after each ride, haha.

Guess I'll order some 105 jets, and put a lighter foamfilter in the future as well.

You don't need bigger main jets, your messing with something which is now going in the right direction. From what you posted I think you just need to richen the pilot air mixture. Turn the airscrews in by 1/4 of a turn. Ride it. If it's still lean go in another 1/4.
Youll then be close to stock settings for a stock bike. This suggests to me your air filter is pretty much as restrictive as a stock one. The exhaust system has an  almost negliable effective on carburation Unless it is overly restrictive. 
When you show a picture of your plugs show them end on so I can actually see the colour of the electrode clearly. Also need to see all 4 plugs. 
If plug one is good it doesn't mean plug 4 is even if the carbs are set up identically. You need to think of the engine as 4 singles each with its own carb initially. Then you need to get those 4 singles to synchronise which each other by balancing the vacuums. 

Allright, thanks for clarifying

In my mind the only way to get it richer was to go bigger on the main jet = more fuel. That just goes to tell how much I know about carburettors though.. learning by doing here
I'll adjust the airscrews underways. There is an old MC-mechanic in town, I'll ask him about vacuum syncing.

My father owns a car-shop and has an exhaust-gas measuring device, I dont know how these things work, but he said it could be used to measure if it runs lean or rich.

The fact that the air filter is close to as restrictive as the original one is awesome (if that's the case). looks alot better and is much easier to remove and mount than the stock one.

The exhaust is basically a straight pipe all the way, it has a little muffler, but close to no restriction there.

I'll check all the plugs, but that'll be for a sunny day.

As I previously mention the pilot system affect the whole throttle range so richening the pilot system (by reducing the air) will richen the whole range albeit to a lesser degree the higher the throttle opening because the volume of fuel and air supplied by the pilot system at high revs is a lower percentage of the total fuel air mixture supplied by the main/needles.
A car lamba exhaust probe is useless as it will only show you the 4 cylinder combined results. You need to know what each carb/cylinder is doing. They each will have different wear to parts (both carbs and cylinders) so need to be set up as if they were 4 singles then sync'd together to act as a whole unit. 

When you want to sync the carbs ask for advice on here or mail me.