So yes, you can gerrymander Senate seats. It's just harder and less reliable than House seats.
I mean, hell, at this point, a lot of "state lines" are either way too far in (resulting in close-by cities within the same broad metro-area having no common government in the Northeast) or way too far out (resulting in close-by cities in the Bay Area having no common government that doesn't also serve rural Central California).
The point of drawing constituency lines is to unite people who have common interests while giving mutual autonomy to people with competing interests. The current states in the USA do none of that: they basically just systematize the shapes of former colonial land-holdings.
[1] https://en.wikipedia.org/wiki/Article_Five_of_the_United_Sta...
The phrase "the Constitution prohibits this amendment" doesn't make any sense because an amendment to the Constitution cannot by definition be unconstitutional.
1. An amendment eliminating all actual powers of the Senate, either with our workout creating some new body to which those powers are transferred, or
2. An amendment eliminating the restriction on amendments eliminating the equal representation of States in the Senate.
What if New Jersey and Michigan just decide they want to be as they are, but excluding Camden and Detroit respectively?
Or would you do something whimsical like draw lines based on football/baseball teams and cleave states like CT in half?