Apparently an actual G3446 replacement can only be found at a garage sale or something. Nobody makes such a thing.
Universal remotes seem to have low probability of emulating a G3446 as the G3446 is so old that it has only 6 dip switches, less than the 8 or 9 in somewhat newer (and still ancient) remotes.
So the smart solution is to buy a new remote and receiver. The easiest solutions appear to be those that replace your wall switch for the opener with one that also contains a new receiver, and then include a remote for that receiver. I'm sure there are other options but $20 at Radioshack is one: http://www.radioshack.com/product/index.jsp?productId=2854290&cp=&sr=1&origkw=garage+opener+remote&kw=garage+opener+remote&parentPage=search.
This should be easy enough that virtually anyone could do it, and the price is right.