Shimming a Floor Joist
If it is possible, use the ripped down 2X4. The built up shingles will work for a while, for I think they would compress over time since the asphalt or the derivative of it will move if given reason to.

If there is no room for sistering a full sized joist beside it, perhaps just a 2X4 glued and screwed to the side? Just in case the reason why it cannot be sistered otherwise is from utilities passing through the way. A notch here and there will get past issues too.