After 6 days and NUMEROUS attempts I have figured out how to get Snow Leopard onto the new Mac Mini!! It turns out I wasn't thinking the problem all the way through. I thought that the Mini was causing the kernel panic when connected in Target Disk Mode. However I was trying to install the retail Snow Leopard (which is 10.6.0) onto the Mini using an MBP which required 10.6.3!
There is a step after all of the applicable files are copied to the Mini (TDM) where the Source machine reboots and is supposed to continue the install. This is where my MBP was freezing up and I couldn't understand why. Well it turns out that the MBP is attempting to boot from the SL disk (10.6.0), however this machine requires a minimum of OS X 10.6.3 so the boot was hanging.
I ejected the retail version of OS X, input the Recovery disk I got with the MBP (which is 10.6.3) and the install continued as usual. Once installed I booted directly to the Mini's hard drive (TDM) via the MBP and ran Software Update to get to 10.6.8. Then rebooted and let the Mini boot itself...and we're up!
1) Put Mini in Target Disk Mode (Firewire only)
2) Put SL retail install disk into Host Mac and install to the TDM drive
3) When the reboot hangs power the machine down (or if you're fast hold down Option on that reboot) and restart holding Option.
4) When the boot choice screen appears eject the Retail disk and input your Recovery disk.
5) Boot to the Recovery disk and the install picks up automatically (don't worry, it's actually installing 10.6.0 even though you're booted into 10.6.3's recovery).
6) Once you've gone through the new user introduction stuff (input username, etc) run Software Update
7) Power down the Mini and restart it w/o TDM.