The thing to keep in mind is that the number at which factorals overtake exponents is low enough that exponents are never worth using. 14 is the first time a factoral overtakes. 9! is way larger than 14 and 9^ is nothing. so 9^9 is severally lacking compared to 9!!.
Now, the only way exponents could win would be with them back loaded. 9^(9^(9^.....))) However I can't prove that even this would overtake factorals. However if it does it would always overtake them...
I don't believe that a mix of ! and ^ is going to be the solution (with the exception of using one or the other to fill a final spot to get to 100 characters without waste (as would be the case in mine if done correctly and with 9! instead of 99 to get the 100th character.)
anyways long story short.... 9^x is lower than x! starting with x = 22. So even with the exponents on the back end factorals win.
Unrealities is the highest number that can be achieved with 100 characters.