Can you change the boot order of a VMware ESXi EFI guest in a config file

According to the docs it should be the "Session Recovery Timeout" parameter. But keep in mind that the guest OS's would have their own timeouts - these might need a change as well.

First, check that you have access to the vSphere vCenter or ESXi server from your client system over the following ports: 443, 902 and 903. This can be verified using telnet esx.server.ip 902 from your client machine. See the full port definitions used by VMWare here.

As for the virtual machines, there are a few approaches to debugging ESXi boot issues. I'd suggest examining the VM's logs from the ESXi console. Assuming you have ESXi console access enabled (or ssh access), you can check the output of the logs in the VM's directory.

For a system like yours, using local storage, the directory path will be similar to the following (assuming a VM named "Virtual_Machine"):

cd /vmfs/volumes/datastore1/Virtual_Machine/

Within that directory, you can examine the vmware.log files. I'd try to correlate the timestamps with your boot activity or possibly tail the most recent log file as you attempt actions on from the vSphere client side.