Due to my OCD I've been upset by the same issue a number of times. All strings gotta run parallel! The problem can be remedied to an extent, or even completely, if one takes care that the last part of the E string to touch the peg (the last few millimetres that are on a tangent to the peg shaft) do
tuck under the previous wounds of the string and
not on top of them (seen horizontally). If done so, the E string is brought as close as possible to the axis of the peg and runs almost parallel to the rest of the strings. To achieve that, while tuning/tightening the string, when almost done, turn the peg so as to release tension and try push/tuck the last bit of the string to touch the shaft of the peg. Here's a pic of my Pbass freshly strung with La Bella 760FS flats (.105 E string).
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