Convert filters pre-trained with ImageNet to grayscale?
I doubt either of your proposed approaches will work, these convolutional layers learn all kind of relationships between the colors which will be non-existent in grayscale, upsampling it to RGB makes your input space very different from the input space that ImageNet was trained on and averaging these filters of the trained ImageNet model makes a whole lot of assumptions that are unlikely to hold. The second approach does seem more promising than the first, so if you want to test an approach I would go for the second one. It's possible that it is at least a better initialization than randomly. I think you will end up needing a lot of data and computation anyway, so it might be better to start off with your own network shape and start from scratch.