Although I understand it is not common to respond to your own question, I deemed it appropriate to still post the following as such, as I did some extra research after I read the other responses. I did this in an attempt to further distinguish the two words.
As i reconstruct the meaning of both words with the help of the etymological dictionary it seems to me that an act historically seems to be slightly more associated with movement and a deed has an historical origin of putting something down, especially in the sense of laying something down/making a mark in history. In that sense it's also logical that it is a very much used word in the juridical sphere as a form of written contract (already in this sense in 14th century). Moreover it helps explain why doing a menial task as doing the laundry may not be seen as a deed, but declaring war on a different country can surely be seen as a deed (as that can be construed as a new contract/breaking of old contract).
act (Proto Indo-European root is *ag- "to drive, draw out or forth, move")
deed (Proto Indo-European root is *dhetis, from *dhe- "place, put")
wasnt able to post the next part as a comment, so posting here. A few questions which I hope some other native English speaker can answer to further distinguish the two words.
1 Would the following examples pass as correct/incorrect english?
- The act of lying down
- The act of standing still
- The act of thinking
- The act of jousting
(Personally I believe all four are acceptable english, though one might argue that the first three might technically be erroneous.)
2 Would the following examples pass as correct/incorrect english?
- killing a man is an evil deed
- walking away from the murder scene, he knew he had committed an evil deed
- Van Gogh cutting his ear off can be seen as a unusual deed.
(No clue if this is acceptable/erroneous English, i would guess acceptable)
3 as i understand it correctly the following sentences are not deemed correct English and the word deed should be replaced by act in the following sentences
- Brutus committed the deed of killing Julius Caesar (historically somewhat inaccurate i know)
- the deed of killing Julius Caesar