mjhjmtu

I'd like to use the first tool for establishing a 3G connection, but the other seems more apt for wifi. Running both together seems like a road to disaster. But how could it stop one completely and make the other run without restarting the laptop? service NetworkManager start doesn't seem to do the trick. And I also need wicd to be closed cleanly, without shooting down essential services that will be used by network manager.

Do you really need to use NetworkManager ?
There's a lot of dependencies = operations that happen when you interface goes up or down (see /etc/NetworkManager/dispatcher.d or /etc/dhcp/dhclient-enter-hooks.d/ or leave-hooks), and also services like dhcp or wpasupplicant for wifi.
What I would suggest you, would be to:
1. remove network manager
2. use wicd for wifi connections
3. use sakis3g for establishing 3G connections.
sakis3g is a binary used to "make establishing 3g connections easily"
Please get familiar with sakis3g package and examples on using it.
BTW,
I myself, removed network-manager completely in office and private laptop, as they used to break sometimes, partially because of problems with systemd whole subsystem.
This way (sakis3g, wicd), you make whole process easy, unless you have little knowledge about command line (running programs from command line).

I found it necessary (over years of unhappy wandering in the wilderness) to remove NetworkManager entirely to get wicd to work at all. My impression is that NetworkManager doesn't play well with any other application which manages the network devices.

And i don't mean just try to inhibit NetworkManager from currently being an active process but remove all its re-plumbing of device interfaces as well. (dpkg --purge network-manager)

I'm sorry that's not giving you the specific response you were after, but I think you could do what you're trying to do with multiple configurations of wicd alone.