As promised, here's my update on the two projects I did around three months ago using Dishwasher Safe Mod Podge! It's a relatively new product and I had a hard time finding reviews about its effectiveness, so I thought I'd share my experience.
I do want to note that I didn't actually put either project in the dishwasher, due to the nature of the projects (coasters, wood cutting boards). However, both frequently encounter liquids.
As you might recall, I applied a coat of DSMP over the paint on the board edges. The painted edges still look like they did when I first finished the project. I use these on a daily basis, always washing them after use with water, dish soap, and the soft side of a sponge. Water just rolls right off the edges. No issues!
I was more nervous about this project because of the papers beneath the DSMP layer. However, they have held up well also! We also use these daily. I did notice that if I put a really hot drink down (i.e. a cup of tea while it's still steeping, so near boiling temperature), the bottom of the mug sometimes sticks slightly to the coaster surface. I just carefully extricate the cup when I notice this and haven't had any problems with permanent damage. Occasionally, rings of liquid end up forming on the surface - one had a coffee ring (looked like a stain) on it. However, even weeks later, I was able to just wipe it off with a damp cloth and there's no hint of the stain remaining.
The verdict? DSMP held up very nicely in both cases! I would definitely recommend it for these projects and any similar ones.