Hey Eugen,
I hear what you wanna do, but my gut feeling is that you’ll be spending a lot of time, effort and money on a patching up a solution that will bring you no closer to your desired outcome.
In short, do consider your desired outcome, and whether you have a plan in place to upgrade your studio over time. As some of your components in the set-up are already reaching end of line when it comes to software updates etc.
Do NOT let the above discourage, it is only intended to be helpful.
On the vMix website there are a whole list of controllers that has been tested:
https://www.vmix.com/software/supported-hardware.aspx#capturehardware
The two brands that is IMHO best known is Elgato and BlackMagic.
Elgato is good if you’re trying to do everything yourself, including being in the front of the camera.
BlackMagic, is BlackMagic – kind of a “lucky dip” when it comes to functionality, but perfectly useful for you. One word of caution on the mentioned “ATEM Mini”, which was used on a music production that I was camera lead on a few years back – camera channel 3 overheated, as it is on top of the power unit inside that mixer – that was the explanation back them.
It highly unlikely that they will have firewire in, but you should be able to get a converter for that too. Or hopefully upgrade your camera to something with either HDMI or SDI out.
Hope that this helps you.
Good Luck, and don’t forget to post links to your music productions so we all can enjoy them!
Atb
Mads