I already some times described my configuration, ...
... in vague terms and you continue to do so. Don't be affraid to get technical, we can handle it. We do not want "IP1" and "IP2", we want addresses, gateways, netmasks, i.e. description like this:
ISP1: network 1.1.1.0/28, default gw 1.1.1.14 (ISP's router), my router should get 1.1.1.1 and ESXi guests 1.1.1.2-13
ISP2: network 2.2.2.16/29, default gw 2.2.2.17 (ISP's router), my router should get 2.2.2.18 and ESXi guests 2.2.2.19-22
Don't want to share your real addresses with whole world? No problem, make them anonymous. But don't invent something completely fake, just take your real addresses and give us x.x.1.1 instead of 1.1.1.1 and y.y.2.1 intead of 2.2.2.1.
If there are some limitations, like you not being able to touch ESXi settings, fine, we can accept that and think about them as blackboxes instead of configurable ESXis. But you in turn need to accept that it might make simple and straightforward solution impossible and some workaround might be needed instead. And it might not be exactly what you had in mind.
Also, are you sure that you did not forget anything? You were attempting to do
something with NAT. So you don't need that anymore, or did you forget to mention it now? Every little detail is important. Future plans are important.