I fully expect someone to point out that this already exists :)

I typically move between tabs using Cmd-Opt-Left and Cmd-Opt-Right. Typically I try to arrange the tabs so that the set of files I'm actively switching between are adjacent. If Cmd-Opt-Ctrl-Left and Cmd- Opt-Ctrl-Right moved the current tab to the left or right I could re- order the tabs as part of navigating to a different tab just by holding Ctrl down.

Say I have four tabs:

[*F1*] [ F2 ] [ F3 ] [ F4 ]

I'm on F1 and I want to go to F3. I'd also like F1 and F3 to be adjacent to each other because I'm going to be switching between them. So Cmd-Opt-Ctrl-Right does

[ F2 ] [*F1*] [ F3 ] [ F4 ]

and then Cmd-Opt-Right does

[ F2 ] [ F1 ] [*F3*] [ F4 ]