1/8 sounds like a fairly thick piece of veneer there, so I'm not sure what It would take to penatrate that deep. I've been told the base of the stain is important to getting all the way through though. I've heard of clothes dye being used before. I think the veneers were soaked for a period of time in a flat pan filled with the dye, and weighted down to sink them, but I've never tried that Myself. I bought some packs of it one time in different colors, believe the brand name of Rit, Ritz, or something like that. I found the stuff at the grocery store I think, and cost was minimal. I had a few different colors. but misplaced them, and lost the desire to try them out. I have no idea how well they would work. Might want to do a search on here on dye and veneers. Seems like there were a few threads that had some good info in them. I don't know what the downsides to water based would be, other then the obvious mix of water, wood and humidity related things that come to mind. Alcohol based stains I think may stick to the surface better therefore sometimes have better surface results, but I don't think penatrate very deep due to evaporation, and I'm not sure about soaking with them, as that could be different. Under normal circumstances Oil based may go deeper, but not sure if that would cause any adhesion issues. Some of my information may be alittle inaccurate, as I'm just trying to remember It at the spur of the moment, but Like I mentioned there have been some threads related to It in the cuemaker section. There are others here that have more experience with It, and could give a better description of the different bases then I can. Hopefully someone can chime in that knows. I think for most people that need common veneer sizes, that It's just easier to Buy them pre-dye, but if someone wanted to do something in a different thicknesss that's not available, then doing theirself may become nessesary.
Greg