I've seen similar things with some other papers on my 3800.
It sounds as if one rear edge of the paper is getting hung on something in the feed system (God knows there are enough bits to hang on if a paper is so inclined) or making slight head contact (ink smudge on paper edge) and acting as a 'brake'. One side hangs slightly, the other side of the paper continues to try to continue fwd, paper skews. Even the SLIGHTEST touch on one edge could cause a skew. The whole printing process is based on the assumptions that the paper in the feed area is a) flat, not changing thickness(swelling) and c) feeding straight and evenly.
It could be as simple as platen gap (I always err on wider than called for side), but if there is ANY curl, I mean ANY, on the trailing or leading edge of a paper (Fine Art Baryta anyone?), it can cause issues. Throw in a platen gap that may not allow much margin of error and away you go.
The 38xx, lacking vacuum hold-down, doesn't play well with papers that aren't flat and/or swell under ink load. Curl on trailing edge SEEMS more sensitive. My guess is that as the bulk of teh sheet leaves the out feed slot and dips slightly to contact the tray, the trailing edge tries to lift - making a slight curl a larger issue.
Try a different paper - something generic and simple - a basic Epson paper that uses PK ink (Bamboo is PK IIRC) and if no issues, you now know it's paper specific. In that case, I'd suggest trying any or all of the following:
-Check for edge curl and if any, see if you can get rid of it.
-Open up the gap - you can go much wider than called for and would need a strong loupe and a very high-def paper to see any difference
-Try supporting the printed area of the sheet as it emerges from the outfeed.
I love the 3800 when it works well, but when you look at the myriad of issues we continue to have (in varying degrees) across ALL makes of printers, new and old, with scratches, paper handling, clogs, ICC's not taking, having the temerity to use non-MFG papers, etc., etc., and bloody etc., you can't help but realize why so many out-source their prints.