Fragmentations and rearrangements in n-(4-alkyl phenyl) alkanoic acids in mass spectrometry
In your update you nearly got to the point: the McLafferty rearrangement from the carboxylic acid can lead to two products, either the ionized acetic acid (ML product) or the ionized alkene (ML'). In this case, ionization energy of the enol tautomer of acetic acid is probably much larger than that of alkenyl substituted benzenes (for instance the closest I could find in structure is o-Allyl-Toluene for which the IE is 7.78 eV). Thus from application of the Stevenson-Audier rule, the charge should remain on the moiety with the lowest ionization energy, leading to the formation of the m/z 188 moiety (ionized p-pentyl-allylbenzene).

This hypothesis is further reinforced as it also explains the formation of m/z 117 from a oss of 71 ($C_5H_{11}^\bullet$) from fragmentation of the m/z 188 radical cation, through a pathway similar to that leading to m/z 177 from the molecular ion.

(This is likely oversimplified mechanism interpretation: I strongly suspect that some other rearrangements or cyclisation likely occur in the process. I did not run a complete database search for other EI spectra of similar molecules, but for instance 10-phenyldecanoic acid leads to only a very minor loss of 60. Thus I would suggest that the m/z 188 probably undergoes cyclization and / or hydrogen migration processes leading other products.)