Del, I cut a 1/2 dozen backing strips this morning on my bandsaw. I use the cheap 1/2 blase with 3 or 4 teeth, the fewer teeth the better. Before you start carefully adjust your saw and make sure the blade is running down the center of the top pulley. Many saws even when perfectly adjusted still require finding the angle of drift for a better quality of cut. Very easy to do. Draw a line of a cheap piece of wood and start pushing it through your saw following the line, when you have run about 4 or 5 inches straight hold your wood still and turn off the saw. Now look and see what angle you are holding the board. If it is perfectly straight your fence will work fine, if not they adjust your fence to the same angle you were holding the board. It will increase your feed time and greatly improve the quality of your cut. But finding the blade angle will effect the cut quality substantially.
I second this to Jupiter and back, and also Adams post as well. For my preference, tablesaws are loud and dangerous, and if your gonna be doing it a lot, a bandsaw is the way to go. Haven't been doing this as long as some, I am just seconding the experiences of the more experienced on here. I use a woodslicer blade, it is a thin kerf 1/2" blade, my bandsaw is a 14" grizzly. I recently bought a 3/4" carbide resaw king, and I still prefer the woodslicer way more. I think I can't get the resaw king tensioned enough maybe. I also will recommend to definitely use a feather board, or something to keep the wood close to the fence. I make a feather board out of wood, they work great, a lot better than trying to hold the wood against the fence while your guiding. With a good woodslicer blade, if you can find the blade angle and set your fence to it (you can also clamp a wooden fence and wedge it to your normal fence if your fence doesn't adjust), you can get a cut quality good enough to glue up. I still like to sand with 80 grit though to help the glue up lams stick together.