Davo,
You’re probably describing the technique here-
http://www.fullnet.com/u/tomg/gooteepc.htm
I’ve been using that for lack of easy alternatives, and have even considered finding one of the laser printers like he uses, so I can print my own. The ones I’ve done have come from a copy machine at my father’s office. I believe the toner is about as important as the paper. The first ones I tried came from a local Kinkos (print shop), and they all but refused to leave the paper. I started off with the “JetPrint” paper Gootee used and then grabbed a pack of the new “Staples” paper he found. The Staples stuff works well, but it leaves a “residue” on the board, which you rub off with finger pressure. The old stuff more or less falls off on it’s own after a bit of time soaking. Rubbing the traces scares me, but he swears by that new paper, and I have had the old stuff pull traces off while I was peeling.
It’s not a bad method, but does take a bit of practice (which it seems you’ve had). I did one of the Willem EPROM programmers with it, and it had a bunch of those god awful traces that squeeze between IC pins, etc. Unfortunately, the exact amount of pressure and time is difficult to log and repeat, but the messy transfers are really easy to wipe off afterward, so you don’t waste anything. It seems every time I do these things I have to spend a about a half hour remembering my previous technique and getting clean transfers, so I try to throw at least a few of the same board on each sheet and bring home at least a couple (the paper is cheap as dirt). It may also be wise to get a few small practice transfers in and then start the bigger one, but my problems are usually at the edges, plus you may get lucky and dump a nice clear one while you’re warming up using the final board for practice. I’ve found that pressing too hard over the full board, or for too long, can blur some of the traces and I now prefer to focus smaller amounts of heat, pressure, and time with the pointed tip of the iron around the entire board over a bit longer total time. I still do the initial minute or two on the full board, but I don’t press too hard. I don’t think that lighter pressure with the tip, moving to different areas for a long time can do any harm, and it may insure that everything makes it to the copper.
I would try different types of copy sources first, assuming you’ve gotten one of the papers he likes. I may have gotten lucky with the copy machine I found. I do think I used a piece of paper over the back of the board when I ironed, but I see masking tape recommended. I’ve also backed the heat down a bit from max on the iron, and the one I use now, somehow seems to do better than my previous one, so you may want to borrow a different iron to double check. You shouldn’t need to follow his exact directions to get a good copy, or even replicate your own procedure each time. The initial attempts should come out fairly close with the right combination of paper, toner, etc.
I probably don’t know enough to check your layout for circuit errors. Hopefully, someone else here could. I have found it beneficial to beef up any thin traces if they have room surrounding them. This keeps them from coming up with the paper, if that’s a problem. I noticed a few skinny ones on your PDF. I also sometimes get pinholes in my larger ground masks from the extra time I spend getting the copper from around the smaller detailed traces, but that’s an obvious “etching” issue.
                       Hope you can get it working! 
                                           George
PS- If you do sort it out, see if you can get good transfers to metal substrates. I’m trying to do that for my current box, but haven’t gotten around to the label stage yet. There’s probably a combination of metal and surface prep that would work for clean black labels.