Congratulations on keeping up with the pumping.
'Snacking' is very much a matter of perception. The senior midwife who ran my birth centre and took my breastfeeding class said you should always offer both sides to prevent snacking and of course this doesn't fit with Tracy's experience and lots of experiences of people on this site! A newborn might go through a spurt and feed every 1.5 hours or even more frequently and that wouldn't be necessarily snacking as long as his mother was responding to hungry cues. Some people would say a baby still feeding every 2.5 hours at 4 months is definitely snacking - others would be perfectly content with that.
What I have been doing is giving him the rest of the bottle. that is if he does not finish it, soon after his nap (he usually naps after his A). Would this cause him to be a snacker? I initially thought that he would eat poorly for his next bottle if I offered him the rest of the bottle so close to his next E, but I have not seen this happen consistently.
To be perfectly honest I'm not sure I completely understand your description. Are you doing EASY? If so, wouldn't he be having his feed after his nap anyway? Are you doing a form of EAEASY? Perhaps if you give a rough outline of his schedule it might be clearer?
I don't think there's anything wrong with doing EAEASY if it works for you and means he sleeps better and is more content.
If you are pumping you may find that his amount varies because your milk varies in consistency through the day e.g. morning milk might be richer and higher in fat content so he might take less.