You seem to be aware that a Whonix workstation requires a Whonix gateway as the NetVM. However, you need certain websites to see a non-Tor connection. So you need to be using a non-Tor browser to access those sites - ideally connecting to a VPN first. If you are going to be using Firefox anyway, why not just use a Debian VM with Firefox pointing to a trusted VPN proxy. Set up the VPN proxy with strict firewall settings and DNS script. Add another firewall VM between the two. Something like:
Debian-Firefox -> web-firewall -> VPNproxy
The VPN proxy can point to your Tor gateway (through another firewall VM). Something like:
Debian-Firefox -> web-firewall -> VPNproxy -> vpn-firewall -> sys-whonix -> sys-firewall -> sys-net
This is a “Tor over VPN” setup (or more intuitively “VPN through Tor”)
In other words, you first connect to your ISP through Tor and then begin sending your browser requests to your VPN through the Tor network. Your ISP knows you are using Tor but the website sees you using the VPN IP.
You could use that configuration for the few places you require non-Tor connectivity with a web service. For everything else use a more ideal setup such as Tor or VPN over Tor i.e. anon-whonix -> sys-whonix -> sys-firewall -> sys-net OR anon-whonix -> sys-whonix -> tor-firewall -> VPNproxy -> sys-firewall -> sys-net
I think the above approach is better than messing with remote desktops and firefox running on cloud servers, etc.