Squeezing more than once is definitly a no go. If it is not correct the first time you have to wipe it and clean with IPA and retry. But you already know that and know you know why
If the soldermask is ok and the amount of paste is ok then it shouldn't matter, the reflow process will let a bit too much paste flow on the pins of the component, unless you really do have an excess of paste.
The problem is probably one of the following:
- the reflow (timing) process (for instance wetting phase is too long the paste can start too move on top of the flux)
- the soldermask is not good enough between the pads
but very tight pitch components can be a PITA