Well, call me a fool but I actually went ahead and fermented a batch with this two-year-old slurry.
I doubled my batch size and split it into two fermenters. One bucket got a fresh vial of WLP029. I didn't make a starter, because the yeast was super fresh and it was only a 3-gallon batch of kolsch.
The other bucket got a big stirred starter of the 2-year old WY2565 slurry. I actually ran that slurry through two starters, just to be sure that it wasn't bacterially contaminated.
The 2565 version has been in the keg for a few weeks now. I just hit it with gelatin last weekend, and now it has dropped brilliantly clear. I have to say that it's really an excellent kolsch. This is only the 4th batch of kolsch that I've brewed, but it's incredibly good. The spritzy/fruity/winey yeast character is coming through really well. The WLP029 version is kegged but still in the pipeline, so I can't do a direct comparison yet.
Maybe I just lucked out with this batch, but I wanted to share my success and let you all know that it is in fact possible to brew great beer with 2-year-old yeast. Advisable? Maybe not. But for me it was worth the small investment of grain and time, and it paid off! Cheers.