I saw something on Kickstarter recently - taking the design of pieces from Chinese Chess (wooden discs w/ character printed on top) but applying Western Chess iconography. Not quite the same as the shape of Shogi pieces, but has the advantage of the pieces being round and hence omnidirectional.
Traditional Chess Set with "shogi-esque" pieces

A wild idea is that you could order some custom poker chips (with the chess piece graphics you want printed on them). I'm still looking around for something that suits what you want more exactly, but that thought popped through my head while searching.
Found this, too:
Which is probably not what you want, but worth passing on.

Another close idea, though I don't see that you can buy this:
http://www.behance.net/gallery/Fablab-chess/11402503

How about getting blank shogi pieces and drawing chess icons on them? You can buy them online.
http://shop.nekomado.com/products/detail.php?product_id=46
For readers reference, I think HIDETCHI's "International Shogi Pieces" are very much like what Drake is looking for. You can see the image of them.
http://shop.nekomado.com/upload/save_image/11050001_4eb3fe412d47b.jpg

Frank is correct about the "kickstarter"(?) set. It was posted in the forums but I cannot seem to find it here or on kickstarter. Maybe it was a different public upstart site. If I remember correctly it was a larger travel set with a roll up (cloth?) board. Good luck to you

For readers reference, I think HIDETCHI's "International Shogi Pieces" are very much like what Drake is looking for. You can see the image of them.
http://shop.nekomado.com/upload/save_image/11050001_4eb3fe412d47b.jpg
Yes indeed. Ancientchess.com had the same set at one point - looks like it's sold out right now, but according to the owner, they are getting it back in stock this year
https://www.youtube.com/watch?v=dFK8zbUkg8k

I found the sets I was referring to...sort of. It looks like the makers have switched to square pieces instead of their round wooden pieces on the original design. It's different enough and interesting enough to possibly pick up a set myself. What do you guys think?
https://www.kickstarter.com/projects/queensquared/the-portable-chess-set?play=video_pitch&ref=search
Not sure if this exists, but I much rather the feel and apparance of shogi-pieces. They are flat, thick, heavy, and very compact.
Basically, I am looking for those pieces with the traditional chess iconography (much like what you see when playing on chess.com). I am not looking for anything that sticks to the board or is designed for demo purposes... I am looking for something to play with.
Does such a thing exist?