OK, the Z wants 5V at up to 2A to power it through the power port. There is another thread here on connecting through the internal battery connections, but I won't cover that.
With 4 AA NiMH batteries, at full charge you get 5.34V (approximately). You do not need the diode to lower the voltage. If you use one, you will lower the voltage to the point that the Z will not use it. On the measurements I made (all with a fully charged internal battery), the Z never used more that 1A (actually more like 750mA), and that was with WiFi and full backlight. If you really want the LED to indicate power on, wire it in parrallel so it won't drop your output voltage. I really like the container you found for your power pack. You can also use a voltage regulator chip (LM7805) and a 7V or greater battery to supply 5V regulated. The 7805 is only rated to 1A, but you can use two in parallel to get more amperage. There is another chip rated to 2A at 5V, but I don't remember the part number. I have used both with good results. At home, my desk is wired for 12V due to a ham radio addiction. I have 75A to play with (and a 124Ahr battery backup system), so I easily made chargers for my iPaq and Z.
For additional information search for "battery" under my name "v-man" and you should find two recent threads about external and internal power packs. Shadow Dragon (not correct spelling) has a very ambitious project using inexpensive lithium batteries hooked up to the internal battery connections. My experience is only about the external packs.
Let me know if I can supply any additional information for you. It may take a day or two to respond though.
V-Man