Maybe try a sleeping bag with arms in it. Might just give enough of a wrapped up feeling. Good luck!

You are right to avoid swaddling if he is getting it up around his head.  You might try another type of material when swaddling.  If it is stretchy at all, no good.  You need something like linen, sheet material (like previously suggested), or cheesecloth.  Something that isn't going to stretch too much but is breathable if you know what I mean.  Otherwise, just deal with a crying baby.  He will get over that want of being snuggled up. 

I stopped with Harrison around the same age as yours.  I am sure it isn't too warm in Chicago at the moment so you may want to get a sleeping bag for him to sleep in.

Good luck.
Angela