Hi DedolaDom and welcome to the site.
One you have described as an adjuster screw sounds like the idle mixture screw.
It is item 7 on this parts view.
https://partsfinder.onlinemicrofiche.co ... TOR%20ASSY.
You will need to check whether it has actually fallen out or if the bike still has the original screw which almost sits flat with the body.
If the bike idles ok then I would think it must be still in there, but you need to check. If it is the original 2004 screw it can be adjusted still but you can easily get burnt fingers. A tight fitting plastic tubing over the splines can make it simpler. You normally seat the screw gently then back it out say 2 turns. This should allow the bike to start. Once the bike is warmed up adjusting the screw slightly either way till revs peak at idle. If you are less that a turn out idle jet is too big. If you are more than 3 turns out the idle jet is to small. Good chance the screw will fall out at 3 turns out.
The idle mixture would have little effect on bogging at high rpm.
Does it feel like it is cutting out or just going flat at high rpm?
I would suggest you check the air filter is clean and not over oiled, ensure you have fresh fuel and a fresh spark plug properly gapped.
These things can effect higher rpm. The carby may still need a main jet change either way if the other suggestions don't cure the problem.
What was the idle and main jet before you replaced them?
Do you know which needle is fitted to the carb and what position the clip is on?