If any integer can be spelled with this structure
one some operation one some operation one
the trick could be simply this: reduce the numbers of letters needed for operations (or use O, N, E as much as you can!).
M,I,N,U,S introduces 4 new letters (N does not count)
P,L,U,S introduces 2 other letters (P and L)
A simple (but symbolic) solution is to represent a operation with a single letter... but this is not a way to "say it in English".
So I propose this structure:
PLUS becomes AND (only two more letters, A and D).
Every integer number N bigger than 1 can be said as
N = ONE AND ONE AND ONE AND ONE...
B) Define the number MINUS ONE as "NOT ONE" (let's say this will became our convention, this is the weakest part!) in order to introduce only one more letter (T)
Now zero becomes
ZERO = ONE AND (NOT ONE)
C) Since every negative numbers is equal to its absolute value multiplied by -1
e.g. -59 = 59 * (-1)
I suggest to use a new word to introduce the operation of multiplication, as in class we often say A multiplied by B as "A dot B" (A dot is one possible symbol to show multiplication in advanced math, instead of x or * or others)
Note that now DOT does not introduce any new letter.
So -3 could be
(ONE AND ONE AND ONE) DOT (NOT ONE)
Notice we have used only 6 letters instead of 9 (and mantaining a speakable structure) O, N , E, D, T, A
Now the last problem: how to "say" parenthesis? With the rithm of speech!
ONE AND ONE AND ONE AND ONE [after this sequence do a little pause] DOT [say DOT as an important word, then a little pause] NOT ONE [say NOT ONE fast, as if would be a single word]
Thank you for this pretty puzzle and sorry for my poor english!