You don't need slicks or DOTs to get under 1:20. Just a bigger rear sprocket to get better drive out of the corner in second, smooth lines (which can be tricky at a patchy track like Cayuga). I myself have just broken 1:20 and I think going forward it will be a combo of confidence riding on the edge (sliding the back mostly) out of corners (which is entirely new to me) and holding higher corner speeds with confidence. My body position needs some slight adjustment too. I still wait too long to whack the throttle open.
Studying track videos helps too, especially the lines of riders who gain on you. You begin to learn where you are strong, then clearly see where you are losing ground or are weak.
Make friends with someone riding 2 to 3 seconds faster than you and follow them around, don't make the mistake of chasing down just anybody who blows past you!!!!
Those 2 guys in my video, the ZX10R leading and Paul following run 1:17s so I hear, and they are within my sight long enough to study their strong points and weaknesses. For example, the ZX10 pulls so hard out of turns 3,4,5, while my TC light blipped once. To me this points to better potential to stand it up a little sooner and crank it a bit more. He also went into 2 carrying more speed. I thought I learned to take 2 and 3 better from my last track day, having studied those videos, but yet again, there is room for improvement.
This track day though I learned to take 9,10,11,12 much better as one series rather than separate turns. I also learned to enter fast in a higher gear. This is was important cause fiddling with dropping a gear then back up again later saved time, and all it took was entering faster with more confidence...so the savings in time were 2 fold....faster plus less time wasted on fiddling with gear changes. Things like that saved me whole seconds at various points on the track.
I think I'll go for DOT, slicks or mods when I get into 1:17 territory.