We used solvent based cement. It was definitely dry enough not to pull up in strings, so it sounds like we may have waited too long. I'll try again as soon as it warms up, and pick up a J roller before I do.
Thanks for all the help.
Your non sticking problem is most likely due to it being too cold. Solvent based glue will work on contact with a long wait time. I've forgotten about parts on occasion, and a few hours went by and they stick. The warmer the ambient temperature, which includes the parts and the glue has a lot to do with flash dry times.
Some plywoods may need two applications, depending on how you apply. The back of the laminate doesn't need more than one. Ideally you want the glue thickness totally as thin as possible as it will provide a "closer" contact.
For pressing down, "J" rollers work good, and so does the corner of a section of wood (the 90 degree edge). It provides a small defined line of pressure. Or, just lay it flat and pound down the laminate with a hammer on a flat piece of 3/4" plywood. Use a piece large enough so you don't smack your hand. An elongated rectangle works good, as it gives you a place for your hand, and a place to pound. Just make sure you hit the plywood every time.
Paint rollers will work, but even the thin nap ones can be a problem. They can stick to the glue and create heavy areas and thin areas. Some short nap roller covers work better than others. Some rollers will separate due to the solvent in the glue. If you use a roller, buy the roller covers that are listed for "adhesives". The home centers carry them.
Other than using a brush, roller, or spreader, a spray gun and cup can be used to apply contact cement. You can use a cheap $20 siphon gun. The brush grade contact cement is similar to spray grade, except a bit thicker, and has a retarder in it. If you can only get brush grade cement, thin very slightly with lacquer thinner. When spraying, you don't want to atomize the mix. Spray it so there is a very fine spitting. The down side is cleaning the gun, but lacquer thinner does a pretty good job with that.
You'll need to have drop cloths, as the spray will get around. Spraying is the smoothest way to get coverage. It's the best way, IMO, to apply gloss laminates to eliminate any bumpy appearance.