I just wanted to conclude this thread with what I found, but what I didn't wind up doing.
After searching online, I found a forum question just like mine. The answer was that there were two holes in the slide out tray, one on each rail, and that you could pull the tray out until those 2 holes lined up with a hex key fitted head screw. Those fittings hold a roller in place on the cabinet portion of the battery holder. It's that roller that is FIXED IN PLACE on the chassis (maybe chassis is a better word) such that when you pull the slide tray out, eventually the rear most rollers on each side of the slide tray are stopped by these fixed rollers so the tray is kept from sliding all the way out.
So, getting back to those 2 holes in the tray which you can line up to remove the two rollers on the chassis - if you can unscrew them using a hex wrench and box in wrench on the nut on the other side, then those two rollers are removable and thus you can then pull the slide tray out of the surrounding chassis.
All of that being said, this is not what I did. Instead I looked at removing the entire chassis/tray but that looked like too much work and I had forgotten to look for these 2 holes and hex headed screws, so I repainted it by simply pulling it out and masking enough so that I could brush on the paint. Afterwards, I remembered the forum question/answer and noticed that in my '99 Marquis at least that's the way this tray worked. I did put a hex wrench on it and if it had turned easily I probably would have taken it out, but it didn't so I said, heck with it. I got the top portions of the tray covered with paint but was not able to apply the paint to the entire bottom areas but mine tray/chassis is still pretty solid still so I feel like I've protected it for a few years to come.
I used the rustoleum "hammered" brush on paint which says "black" but is a dark pewter sort of color which looked great even when contrasted with the black areas not needing paint and this "hammered" paint is hidden anyway once you put the batteries in.
So, just for those who would like to remove their trays, once you have the batteries out, if those holes are in your rails and you can line them up with a hex screw holding in the two rollers, then I am pretty sure you will then be able to remove the tray. In my case the trick will be to free up those screws first.
Mike