Does methanol fixation deform cultured cells?
Yes, fixation of almost any kind can have effects on morphology.  When you take a free flowing, protein spiked fat-blob (ie cell membrane), and make it rigid, you are going to get some differences.  

A fun visualization of this can be done by wrapping cellophane/shrink wrap around a serological pipette and dipping it in a dry ice and methanol bath.  It's something I show students all the time before getting into histology work.

Back to what you need.  What cells are you using and what are you growing them on?  Have you tried acetone fixation and you know it destroyed your plastic?  The amount of time and concentration needed for acetone fixation is low enough that most modern chamber slides can handle it.  Do you need the membrane to be permeabilized in fixation?

I don't know the main effect you are measuring, but assuming you have good controls, you should be able to see it past the fixation.  The effect in your controls should be similar to your treated groups, unless the treatment is specifically effected by your fixative.

Moving to some more general recommendations.  I think you should reconsider the fixative’s you’ve ruled out, because I am unconfident about their application.  The base source I always recommend students to turn to is the Wiley "Current Protocols in X" book that is relevant to the task at hand.  In this case, I think the most relevant text is Current Protocols in Immunology, and the appropriate unit is 21.4 "Immunohistochemistry."

I think a particularly useful, and relevant to this question if you are concerned with formalin masking, is Table 21.4.3.  



That is for human antigens, but the “antigen retrieval” process works for murine cells in most cases.  You are right that you antigen could be blocked by formalin, but the solution is often unmasking as MtOH are often more harsh to morphology.  To support protocol 1:


  Formalin or paraformaldehyde fixation cross-links protein, often
  making antigens inaccessible to specific antibodies. The antigen
  retrieval protocol, which combines high temperature with buffers at
  different pH, has been very effective in unmasking antigenic
  determinants which may be masked in fixed tissue or fixed cell
  preparations, particularly determinants within the nucleus or
  cytoplasm (Taylor and Shi, 2013).


My modification of the protocol is:

Sodium citrate buffer: 0.1 M citric acid/0.1 M sodium citrate, pH 6.0


Wash sample on a liner rocker for 5 min w/2x culture volume of d.i. H2O
Place your slides in 1mM citrate buffer in Coplin jars with the lid slightly off
Weigh the jar in final state so you know how much water to add back
Microwave 4-7 min.  You don’t want it to go to a boil, and you need to remember to allow for venting
Weigh the jar again and add back water
Microwave another 4-7 min, again you don’t want a boil
Take out of the oven and allow it to come to room temp by sitting it on the bench.  If you do it too fast you’re going to disrupt the membrane.
After it’s back to room temp, wash 2x PBS+0.05% Tween20 for 10 min each
Try your IHC again, it will probably work now.