Ok, I think I have somewhat of a handle on how these remote models work...
First off, the post that I was trying to find earlier, that has some useful pictures and charts:
how-to-pick-a-factory-remote-t559107.html
And a page that has the Infiniti chart and all of the referenced pictures of remotes:
http://www.infinitihelp.com/diy/common/ ... /index.php
The date ranges in the Date column are a bit confusing since there's some odd date overlaps, but based on the fact that yours was manufactured in June 2000 and the Model/ 01A (2W612) remotes aren't working for you, I'm going to say you need a Model/ A (2W611) remote. The bad news is they're apparently much harder to come by than their 01A brothers.
All that being said, there's another thing you can consider giving a try. I have an 01 QX4 that was manufactured in November 2000, and according to the charts, the 01A should (and does) work fine for me. However, before I knew about this remote complexity, I went out and bought a KBRASTU15 (5W500) and it worked flawlessly. I bought another and it also works great, though it would appear they shouldn't! So, if you're up for a bit more experimenting, getting one of those may work for you too.

The model number on the back of both of mine is MSRA16. They're much easier to come by.
Which guide here did you buy the two remotes based on?
Assuming the smart entrance controller unit is actually working, at least one of those two will work for you. Those units control other things like the defrost timer, interior lights, warning chime, and a number of other things so I would think you would be having other problems if it was really defective. If you want to do some troubleshooting on it though, check the EL section of the FSM, page 319.
By the way, we have some crazy heavy vehicles! 5300 lbs!?! It's amazing they get around as quickly as they do.