You really favour the Rangers in this

It would cost way more to jump THAT many spots

Zero shot the sabres do that.

It says any team in the top 15

well the rangers pick is predicted 16-32 so im saying to move up to top 15 like 10-15 so i dont think its too far off

which trades specifically?

FYI, the 30th pick is reserved for the losing semifinalist in the playoffs with the better regular-season record (and 29th goes to the opposite-conference semi loser).

So unless the Rangers make it to the third round, the highest their pick will be is #28.

Georgiev doesn't get you that, no chance a rebuilding team like Buffalo gifts you Lambert for Barron and Chytil (no chance Lambert calls to 11 either), no way in hell LA lets Turcotte go for that. Just because Kravstov doesn't want to be in NY doesn't mean he has insane value

Turcotte will cost you K'Andre Miller.

Chytil, I don't want anything to do with him, he has good skills and good size but he is a dog, I'm surprised he doesn't get beat up in the locker room.

Turcotte won’t be traded for a winger.

I read this post early this morning and without much thought gave it a thumbs down.
Chytil and Barron are both Left handed forwards, who are listed as centers.
Thompson, Krebs, Mittelstadt, Cozens, Girgensons are all listed as centers, so that is not a need for Buffalo.
Even if Thompson were to move back to RW Buffalo still has 4 players to fill out their center position (even Asplund is listed as a center so it could be 5).
Buffalo has Tuch, and Quinn (Okposo will be gone in a year) as possible RW.
In addition to RW, Buffalo needs RHD as only Jokiharju is signed for next year and only Laaksonen as a decent prospect.
To the point, I was initially presuming Buffalo's pick would be among the top 5 and the Rangers would be 25 or higher.
Then I read you were looking to move up from 20 (as you posted the Rangers pick would be between 16 and 30, I was sort of choosing the mid point of 20) to about 10 (again the midpoint of 5 to 15 as you wanted).
So I started to reconsider and thought if the Rangers were willing to part with a RHD defenseman whose upside was similar to Barron, I may work.
Go to https://dobberprospects.com/team/new-york-rangers/ and you will see Barron (6.5/7.5) has about the same ranking as Schneider (5.5/7.7) first number is NHL upside, second is NHL certainty.
The Sabres unfortunately do not have any game breakers in the line up, if they thought some one on the board could be that player they would not want to deal away a first.
But if they thought the only players remaining were going to be 2nd line forwards, or 2nd pairing defensemen, I could see them moving down from 5 to 18 if the Rangers were to offer Pajuniemi and Schneider.
RW and RHD prospects, both who are predicted to have slightly lower ceilings than Chytil and Barron but fill the holes in the Sabres prospect pool.

EDIT:
I know I give very long answers, but I like to explain my thought process as well as Buffalo's needs