Metho's going to evaporate quicker than water so you could have issues and leave tide marks as a result. Have a look at Nitroburner's build diary here, where he mixed metho and turps together to thin some poly finish out. The same 50:50 mixture of metho and turps should work with your powdered dyes, and allow you to work the stain more like a water-based dye. Using slightly more turps than metho should give you a longer working time and allow you to apply with a slightly dryer rag. But as always, test on some scrap wood first.