Today I noticed something which in hindsight is rather obvious, the problem is with the mainmast but not so much with  the foremast. The difference is the lazyjacks. On the foremast there are lazyjacks forward and aft the mast with little weight on the mast line. On the main most of the weight is on the mast line pinching 

the sail and battens very hard against the mast. I have an idea for how to fix it, will try rigging a lift on the other side to form a basket so there ought to be less pressure against the mast. Next time I'm shopping will check the dollar stores for cheap rope as well. 

A thought: silicone grease or silicone aerosol spray will probably bring some short term relief whilst you find a long term solution.

After trying different things, I now have closed cell foam wrapped around my battens, yard and boom, using duct tape to hold them in place, then covered with an acrylic sleeve I sewed up by hand.  The acrylic is chafing a bit but is easily replaced.  I still have a lot of noise in my alloy mast though, especially when sailing, which seems to come from the yard hauling and luff hauling parrels under tension.  If there is a steady wind and an easy sea, the noise is minimal, but in lighter winds when the sail starts to lift, it's really loud.  I have discovered that I can get used to any background noise when sailing, if I just ignore it long enough, especially as I am a solo sailor and always keep one ear cocked for strange noises when sleeping.  I do like a quiet night at anchor though.  I have a line from the fwd end of the boom that goes around the mast and back to the fwd end, to hold the boom aft (not sure what you call it) and this remains under tension when the sail is lowered, and will squeak like crazy with the slightest movement of the bundle.  The only way I can stop the noise (when rolling at anchor) is to tie my bundle off firmly to stop it moving.  I find the easiest way to stop the furled bundle moving is to tie the bundle off to one side then put tension on the sheet to counteract this.  For me, this has the added bonus of exposing the solar panels on my cockpit roof to the sun.  Bliss...now if only that yappy dog on the nearby boat would shut up!

Another little trick for ensuring a good night's sleep - and one only possible with an unstayed mast - is to wind your burgee halyard four or five times round the mast in a spiral, outside of the main halyard, lazy-jack downhauls, mast-lift, etc.  Stops lines slapping against the mast, whatever the weather.

It sounds as though your batten anti-chafe tubes are made from plasticised PVC, which has a high coeefficient of friction, resulting in squeaking. Some of the harder plastics are better for squeaking, but will tend to tap, instead. I use black plumbing wastepipe, which is available in the UK at 32mm and 40mm diameter. I believe it's ABS plastic. Polythene water pipe has a low coefficient of friction, and may be soft enough not to tap, but unless it's black will be vulnerable to UV damage, eventually. Ex Fire Service hose has been used successfully.