NOTE: The rules have been updated to cause the nature of the puzzle to be as intended. I will upvote the answer which was given before the change, but I look for both alphabetic and math operations to be used to solve the puzzle.
There are the kinds of puzzles where you take a number and try through math to get it to another number, or start with letters, and try to get to another word through a series of valid words... but what about a combination of the two.
(15 14 5) Starting with the letters: _ o n e_
and changing only one letter at a time or converting the letters to numbers, apply one mathematical operation specified below, you must follow the path of:
one $\to$ two $\to$ three $\to$ four $\to$ five $\to$ six $\to$ seven $\to$ eight $\to$ nine $\to$ ten
Each result of a letter substitution must be a valid English word. When converting to numbers, the results of the math do not need to be valid words when applying operations, but must be to switch back to letters (which must happen for each of the goalpoints).
Valid math operations: (all except rotation of numbers to a single characters digits)
$+1$,$-1$,$\times2$,$\mod27$,sum the digits (14 $\to$ 5),multiply the digits (14 $\to$ 4) rotate numbers clockwise or counterclockwise (15, 14, 5 $\to$ 14, 5, 15 etc)
Valid alphabetic operations:
add a letter, remove a letter, rotate characters clockwise or counterclockwise.
I will allow for roughly a month if there is interest and will accept the shortest path as the answer, with upvotes for partial solutions. Good luck!
Note: The switching of characters between numbers and letters does NOT count as a step, so does not penalize you.