You could try increasing the buffers in the advanced options of the individual Squeezelite players. You can find the different command line options here: https://www.max2play.com/en/wiki/command-line-options-for-squeezelite/
Apart from that, I can only recommend that you have a look at the slimdevices forum, as this is probably a Squeezebox server problem and not directly related to Max2Play.
Please also check again whether streaming works better with smaller files than with larger ones, because of the network load.
Does the problem also occur when you run only one of the two Pi 2s?