There, I fixed it (with rope)

05AB1E, 38 37 25 bytes

Saved 10 bytes with suggestions from Magic Octopus Urn and another byte changing output format.

Outputs a list of strings.
Footer pretty prints.

'ÙºUζεDÇ¥<)ζε`FX¬sÀU}J]Jζ

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Explanation

'ÙºU                       # store the string "rope" in variable X
    ζ                      # transpose input
     ε                ]    # for each transposed row
      D   )ζ               # zip the row with
       ǥ<                 # the decremented deltas of its character codes  
            ε              # for each pair of [letter, delta-1]
             `F     }      # delta-1 times do:
               X¬          # get the first letter of X (originally "rope")
                 sÀU       # rotate the letters left by 1 and store in X 
                     J     # join the rope-letter to the current row-letter
                       J   # join to list of strings (the new columns)
                        ζ  # transpose

Jelly, 21 bytes

ZµOI’R“¡nⱮ»ṁż@"µF€z⁶Y

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Explanation

ZµOI’R“¡nⱮ»ṁż@"µF€z⁶Y  Main Link
Z                      Transpose the input so the columns are now rows
 µ                     New monadic chain
  O                    [Vectorizing] Convert each letter to its character code
   I                   [Vectorizing] Get the differences (gap size)
    ’                  [Vectorizing] Add one
     R                 [Vectorizing] Range from 1 .. x
           ṁ           Mold the string        into the ranges
      “¡nⱮ»                            "rope"
            ż@"        Vectorizing zip the rope strings with the original string (place ropes in gaps)
               µ       New monadic chain
                F€     Flatten Each
                  z⁶   Zip and fill with spaces
                    Y  Join on newlines for output

-1 byte thanks to Mr. Xcoder
-2 bytes thanks to Erik the Outgolfer

Python 2, 197 194 bytes

def f(s):
 r='ROPE'*len(`s`)*9;x=[]
 for i in zip(*s):
	x+='',
	for c,C in zip(i,i[1:]+(' ',)):l=(C>c)*(ord(C)+~ord(c));x[-1]+=c+r[:l];r=r[l:]
 print zip(*['%*s'%(-max(map(len,x)),s)for s in x])

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• -3 bytes thanks to ovs