I think you’re just about there with an answer. Assuming each occurrence is weighted evenly you could approach this a few ways:

1. Use binary labeling such that the output vector looks like [0,0,0,01,0,0…, 1] and is of length 350. You can think of this as representing the true goal of finding the exact positions. Then, during optimization, you can determine a threshold or other logic to handle all of the fuzzy predictions that will inevitably result from training.

2. Assign fuzzy labels scaling inversely with the distance from the target point. EG [0, 0.1, 0.5, 1, 0.5, 0.1, 0…]. The same thresholding can be done here as well.

Assuming locale is important for classification, I’d consider using convolutions as well to extract useful information from neighboring data points.