JavaScript (Node.js), 101 bytes

M=>!(W=m=>M.every(w=>[m-=(x="ifljIr't?-".search(w)%2+1||3+(w in{m,w,M,W})+(w<{}))]*[m-=x])*m)(W``/-2)

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Python3, 313 bytes

A='abcdefghijklnopqrstuvxyz'
M=[a:="ilI'",b:="fjrt-",{*A}-{*a,*b,*'mw'},{*A.upper(),*'mw'}-{*a,*'MW'},'MW']
E=enumerate
def f(s):
 S=sum(c:=[[j for j,a in E(M,1)if i in a][0]for i in s])
 l=max(i for i,_ in E(c)if sum(c[:i])<=S/2)
 return(U:=sum(c[:l]))==S/2 or((A:=U+c[l]/2)+(B:=sum(c[l+1:])+c[l]/2)==S and A==B)

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Jelly, 52 50 bytes

Œuðẇ⁾MW+=
ẇЀ“fjrt“il-“I'”T_@Ç+3µ€Hx2FŒṖṖLÐṂS€E$€Ṁ

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Although slower and more memory hungry than the below 50 byte alternative that borrows the reduction method from fireflame241's answer:

Œuðẇ⁾MW+=
ẇЀ“fjrt“il-“I'”T_@Ç+3µ€Hx2F+\©ð_ø®ṪHµẠ¬

How?

Œuðẇ⁾MW+= - Link 1, character index offset helper: character list c (of length one)
Œu        - to uppercase
  ð       - dyadic chain separation (call that u)
    ⁾MW   - char pair literal ['M', 'W']
   ẇ      - sublist exists in? (is u in there - True if c is 'm', 'w', 'M', or 'W')
        = - equal? (vectorised u=c? [1] for uppercase or non-alpha c, [0] for lowercase c)
       +  - add the two results (vectorises)

ẇЀ“fjrt“il-“I'”T_@Ç+3µ€Hx2FŒṖṖLÐṂS€E$€Ṁ - Main link: character list w
                      µ€                 - for each c in w:
   “fjrt“il-“I'”                         -   list of character lists: ["fjrt","il-","I'"]
ẇЀ                                      -   sublist (w) exists in, mapped across right
                T                        -   truthy indexes (gets [the index at which the character was found] or an empty list)
                   Ç                     -   call the last link (1) as a monad
                 _@                      -   subtract with reversed @rguments
                    +3                   -   add 3
                        H                - halve (vectorises)
                         x2              - times two (repeats each list)
                           F             - flatten into a single list
                            ŒṖ           - partitions (all ways to split the list into contiguous slices)
                              Ṗ          - pop (remove the right-most; the only one of length 1)
                                ÐṂ       - filter keep those with minimal:
                               L         -   length
                                     $€  - last two links as a monad for €ach
                                  S€     -   sum €ach
                                    E    -   all (two) equal? (1 for a split, 0 otherwise)
                                       Ṁ - maximum (1 if any split was possible, 0 otherwise)

Jelly, 79 bytes

“¡-Ị’b26
“µııẈḟ(µ⁹\fy¦°Ẓ=ȮH@Q0Ẋƈẏ9Ė=ẹṬɗƇ’ðœ?øØa;ØA;⁾'-ð,ø5Rx¢
¢yHx2+\©ð_ø®ṪHµẠ¬

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Retina, 88 bytes

T`MWi\lI'`551
T`-fjrt`2
T`m\wL`4
T`l`3
\d
$*1 
+`^ ?1(1* 1*( 1*)+)1 ?$
$1
^ ?(1+) \1? ?$

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