The springs would be the area I would start if all else failed. If it is an upwelling or a small creek, the different water temp would attract fish. The way it sounds is the walleye in this lake are roamers. They do not tend to school until spawning time. There is a lake around here that is only 9' deep with roamers in it. The best bet is sitting tight and fish. Use lures with flash, bright colors, and most important sound. Try jigging a Rat-L-Trap or the like and when they come in to see what all the commotion is switch to your usual walleye lures. When jigging the R-L-T just pull it up(vary speed on lift to find what works) a foot or so and let drop, wait two or three seconds and do it again. Then don't do anything for 15-30 seconds. Also you can just do quick shakes for a couple seconds and pause. Depending on their mood they could show up immediately or in 15-20 minutes or even not at all. The ones that do show up tend to be the aggressive fish.
Do not be afraid to try new things.