Questions about test topology issues (LTM on ESXi)

The topology looks like this:

-one local network (192.168.1.0/24) with a an ESXi host

-2 webservers and 2 F5s set up as virtual machines on ESXi

-local router is unable to route between local/virtual networks

The idea is to have the servers on a separate network (let's say 10.0.0.0/8) and be able to access them from my local network via a Virtual Server.

What seemed like a simple task proves to me as a challenge. At first I set up the LTMs to use the management port and the default gateway of my local router and created a VLAN and self ip in the 10.0.0.0 network. However this way I am unable to connect to the nodes (because there is no routing between the networks).

So I set up a virtual router and configured the LTMs to use the virtual router as default gateway on the 10.0.0.0 network. This way I am able to communicate with the nodes but the Virtual Server ip doesn't seem to be forwarded to the local network.

Is it possible to have nodes on a different network than the Virtual Server without routing between them?

If I do need the routing is it better to set up LTMs on the same network as the nodes and do I need nating in that case.

Or is there a simpler approach to set this up (still using two networks).