Senate seats can't be altered much shifting the lines on the map because there's two per state, what you take from one you give to the other
Senate seats are ALWAYS state-wide elections, with no district lines to draw or gerrymander. Gerrymandering still arguably has an impact on senate elections, but it's a secondary factor of reducing turnout and not a primary factor of just picking the best districts.
I actually usually feel the same way as you about most trick-taking games, so I usually avoid them.
I did play "Scout" with my group a couple months ago, and found it to be pretty good, so you could give that one a try.