How would increasing the dpi affect a greyscale print at say 10x8 inches
Well, the less dots, the more the white paper is visible between them. My Canon 1000 always prints at 1200dpi and it takes quite a powerful loupe to see the dots. The Epson 3880 I believe has about the same maximum dot resolution.
Suffice to say, at normal viewing distance, Most people can't tell if it's an inkjet print or not.
Even if I could, I would never print at such a low resolution as you are suggesting, since 360dpi only lays down 1.5 dots of ink for each pixel at 240ppi which, on a greyscale, would lead to possible interpolation problems for partial dots/pixels and, thus, possibly irregular graduations.