In order for the USB keyboard to work in Linux (2 stage), Linux loads a USB driver. It's possible that driver is leaving the USB bus in a state that the next ISO isn't able to access.
Can you please tell me which Intel AMT computer models and KVM software you're using? I will try to reproduce it using the same setup.
I have tested this out on an HP 8200 Elite SFF that has AMT Firmware Version 18.104.22.1683. I have also tested this out on an HP 8300 Elite SFF that has AMT Firmware Version 22.214.171.124.441. I was using the Intel vPro Platform Solution Manager and VNC Viewer Plus to KVM into the machines.
That is along the lines to what I was initially thinking, it might be related or a separate issue but on a normal boot if the computer was powered off improperly and boots to "Start windows normally or Launch start up repair" you are also unable to select either choice as well with VNC Viewer Plus.
I decided to create a new Win7PE SE boot disk that will boot directly to the disk without a prompt. When I boot directly from the disc everything works correctly. When I attempt to boot using the ifast.iso it hangs when trying to load into the win7pe.iso and then doesn't load the customization that I have loaded into the win7PE.iso. Specifically I had a simple .bat file on the desktop and we use Symantec ghost to image and have loaded these into the into the win7pe.iso. Anyone else experiencing anything like this?
I just noticed this post. When booting via 2 stage, WinPE can not see the 2nd stage ISO without a special driver. My guess is that your customizations are not stored in the boot.wim file but rather just on the ISO file system. So, you could either move the customizations (and anything else you need access to) into the boot.wim file. Or you could try to add a driver that can expose the 2nd stage ISO, such as firadisk or winvblock
I've successfully used Firadisk 0.0.1.30 for this purpose (FiraDisk (latest = 0.0.1.30) - FileDisks/RamDisks: Firadisk, etc. - reboot.pro) with WinPE 3.1 32 & 64 bit. When I did this I found that using DISM to include firadisk did not expose the 2nd stage image. Maybe I was doing something wrong. What did work for was me was to place the firadisk drivers in boot.wim at x:\firadisk\ and then loaded them via startnet.cmd with "devcon install x:\firadisk\firadisk.inf root\firadisk". With that, WinPE could see the 2nd stage ISO. Note that this may or may not work for you. I have no experience with Win7SE. Good luck if you try it, and please let me know how it goes.
BTW - if this were my imaging scheme I would place my tools and custom batch scripts on a network share. In my WinPE I'd have startnet.cmd map the share with the net use command and then call the batch scripts and tools from there. This way the PE image is as small as possible for faster booting and I could change the tools and scripts without changing the PE image.