I don't have any experience with Invaders, but 81-7 has the same housing as 707 and it is 7 string version of 81, just like 707 is 7-st. version of 85.
This is incorrect!
The 707 is not a 7 string version of the 85. It uses the same type of magnent as the 85 but is voiced a bit differently.
The 707 is voiced between the 81 & 85, its basically 70% 85 or something. The 7-81 is also not a clone of the 6 string equivalent, its pretty much 80% 81 and 20% 85. This is what i've been told, and after hearing both i'd have to completely agree