I can't get an F major scale run without screwing it up at the moment where I slide to F note on 10th fret of G string. First run is E Mixolydian – goes just fine. Second – F Ionian – can't get it. 1st, 2nd and 4st 16th note triplets are played with following pattern (hit, hammer-on, hammer-on) except that 3rd one that shifts position (hit, hammer-on, slide). Maybe you can suggest me something about how to better play it without messing up the note sound and scale structure. Here's the run (second one after 4/4 bar rest) that I've written a tab for..
Are you trying to play it at tempo without working up to it?
This is always the problem. Regardless of how skilled you might be every new thing needs to be "programmed" into muscle memory, even if it seems like it should be easy.
Also, you have provided great detail regarding how you attack these notes but not where the real problem seems to be. For example, is it your left hand fingering that gets screwed up or the right hand has a hard time attacking the next pattern after the slide? Or, is it synchronization between the two hands?
No matter what the issue the process for getting it clean is (1) slow it down very slow, (2) drill the problem spot until you cannot do it wrong, (3) start speeding up, (4) when you get to a speed where it breaks down back off and start going up 2 down 1 in speed until you fly past the speed where it breaks down.
You may be looking for a new fingering or advice to eliminate the slide (which I might try). But the fact is if you are patient you can train yourself to play this at tempo.
You could help us help you by answering the questions I've posed in the comments and I'll update my answer to address them. Last but not least, is this an original composition or a cover tune? Are you trying to arrange something and you have freedom to do what you want or do you need to be on point with this tab?