I am a recovering string hopper. For the past decade, I have learned many lines, scales, arpeggios, and whole solos from many players such as Oz Noy, Frank Gambale, Pat Martino, and Guthrie Govan. I learned many of these lines using terrible technique and in many cases the combination of this vocabulary requires quickly alternating between all three forms of picking. How do I patch together a working improvisation system?
If you can afford it, find a teacher.
Mindful practice,each one of us has unique learning system
I suppose you know the fretting hand positions of these licks/arpeggios/solos you mentioned,now its a matter of practice of the picking hand
Pick a favourite line or a solo where you know you have a tendency to string hop and break it into segments where you can practice your new picking technique
As for speed give it a try with moderate speed(again one where you feel comfortable to burn in your muscle memory the new technique) and then speed it up to combine the segments
I think that’s somewhat of a starting point,and with time your new technique should get into your other speed parts of your choice
Best of luck man!