Generically 7 speed was made to add 1 cog in the space available for 6, and 8 was wider. adding 1 more with the cog spacing of the 7.

so 8 with a block out of one detent, will stand a better chance , as the inter cog spacing is similar ,

Given 6 is wider spaced between the cogs .. like the 5 speed freewheels before It.