Is there a multi-tabbed terminal emulator for macOS that can be run with a different $SHELL on each invocation?
This answer is not using $SHELL, but achieves the same result and more easily.
iTerm2 profiles, as well as setting colour scheme, can use a specific shell for each profile.
As an example I have set the builtin Red Sands profile to bash and not the default login shell (zsh).
In the menu choose Profiles -&gt; Open Profiles.

Add profiles or modify them with &quot;Edit Profiles...&quot;. Here is Red Sands with a custom shell.

Now return to the main iTerm2 window and, in the menu bar, choose Profiles -&gt; Red Sands.  This opens a new tab running bash.

Taking this a step further (you want to run ssh for remote access) you can run a command when starting the shell/tab. Here I have added an ssh command to my Red Sands profile.

So setup however many profiles you want for the different shells and actions you need.
Note: My iTerm2 expertise is at the beginner level. I am sure you can do much better than me and, if not, someone else will have a better answer.