One of the old meanings of 'plaster' was 'to load to excess', as in "Her make-up was plastered on." It was easy, then, to transfer that to mean 'to load to excess with drink'. 'Plastered was first used in this sense in the early 1900s.
All too human, sadly, Treacle! What I have, rather than immortality, is a wonderful collection of reference-sources gathered over decades. That, plus the fact that I'm retired, which gives me the time - a luxury most of the rest of the contributors here probably don't have - to find things out. Thank you kindly for what I take to be a compliment.