The crossbar supports, are they simply resting in the recesses in each side? Those tabs that appear to keep them from coming out of the recesses, can you depress them and then lift the long side of the arm out of the notch?

Yes, the crossbar supports are resting in the recesses in each side. I can barely pop one tab with screw driver, and while a helper keeps it from going back down, I tried to try pop the opposite one is near impossible as the pressure from the center bracket holds it down very tight.

I also feels like I need to sacrifice the middle bracket by sawing it off with saw zaw at this point, but I thought I should ask first as it is an illogical design.

I can't see it from here, but I think you need to remove that middle vertical piece first. My guess is that is snaps in place. Unsnapping it may require some finesse. Assume that it rotates 90*. It may release from the top (push down on the two bars while looking closely and rotating the right direction) using a flat screwdriver (padded to keep from scratching) to pry up between the vertical piece and the roof of the cabinet.

what's holdup up the middle piece is actually the same 2 supports on its bottom, This picture here shows by the arrows, one can zoom in pic by dragging the positive/negative symbol on the bottom right of pic.

I'll get a better and close-up pics tonite, along with the bottom-up view of anchors & clips of the middle piece that you guys can't see and will understand my almost catch-22 dilemma with them.

http://www.box.net/shared/1dn0k6ihq4#/shared/1dn0k6ihq4/1/82072424/715908658/1

what holds that middle vertical piece to the 'roof' of the cabinet?

Refrigerator disassembly can be a challenge, seems moreso than other appliances. I recently replaced the evaporator fan on my GE Arctica SxS, and the rear panel largely had to be flexed in half to get it out due to obstruction by shelf support rails surface-mounted on the freezer sidewalls ... not to mention removal of ALL the interior shelves and drawers, the light sockets, ice dispenser drive motor assembly, ice maker & wiring harness and air deflector shroud (on which two screws are BEHIND the evaporator coil). The deskjockey engineers who design these machines clearly don't ever work on them.

I would think that what you would want to be doing is snapping the long, or right, side of the cross supports up out of the recesses, then bias them forward far enough so that you can go DOWN with that end. Once you have one end free and hanging down somewhat it will take the tension off the other side and on the upright drawer support.

Basically, they went in intact and they should come out the same way. Wish I could see this one in person! Good challenge! Best of luck and let us know what you ended up doing!

Can you bias the front rail down far enough to free the plastic nub from the hole in the top of the rail? If so, perhaps you can then tilt the center guide to one side or the other. I still can't see what is holding the center guide in position on the ceiling of the freezer, though, so can't suggest which way to move it.

I'll try mojavean's suggestion on snapping the long side. In the meantimes, here are 3 more close-up & bottom-up views of the support & center unit as promised.

Bottom views:
http://www.box.net/shared/74ryzl1go7
http://www.box.net/shared/x10n4b7a9m

Center guide:
http://www.box.net/shared/szru4rs33d

If all else fail, I'll adjust my sacrificial process by just cutting off the front support instead of the center guide as it is faster (1-2 saw zaw cuts) & cheaper ($16+ shipping) to do.

Thanks, I'll try to bias the front rail down far enough to free the plastic nub tonite along with the prioer suggestion.
One would think there is something like a screw is used to hold the center guide in position, but I did not see it. This diagram (see part 145F) confirms that there's nothing holding it place other than the 2 bottom supports per our pics.

http://www.searspartsdirect.com/partsdirect/partsdirect/showSubComp.pd?imageUrl=http%3a%2f%2fc.searspartsdirect.com%2flis_png%2fPLDM%2f50025547-00002.png

I'm pretty sure that 'center guide' snaps in place at both the bottom and the top. The trick I think is to get it loose at the top. The diagram does not show whatever holes exist in the case at the top for the center guide to slip into.

Wait a sec, is that little plastic tab facing the front at the bottom front of the center guide a lifting tab that will release the thing from the bottom support hole?

Thanks for those who helped & encouraged. But weedmeister got it right when you said: the 'center guide' does snaps in place at both the bottom and the top. The trick I think is to get it loose at the top.

I finally able to do that last night by pulling down the center guide while did a gentle hand "karate chop" on the bottom of the guide until it has enough room to give a way from the support bars. Turns out there's a groove on the top of the center guide. Thanks for all your help. Here is the picture of the post-removal of the groove and the center guide.

http://www.box.net/shared/k4nmknhlvt
http://www.box.net/shared/4j9y18js0m

Better news is I was able to get the fridge working again ( for now as I'll need 48 hrs to confirm) by replacing this controller/sensor:

Part replaced
http://www.box.net/shared/tiao79775a

http://www.searspartsdirect.com/partsdirect/part-number/Kenmore-elite-Parts/Refrigerator-Parts/6615JB2005H/0046/795/Model-79575546401/0583/0161000?keySuffixId=NA&productTypeId=x&searchModelNumber=79575546401&subCompDesc=Case%20parts&brandDesc=KENMORE%20ELITE&modelDesc=REFRIGERATOR&pathTaken=partSearch&blt=11

WTG, Weedmeister and Warren. Thanks for posting your findings, too, glad to know you got into the thing and could replace the part. So is that part actually a thermostat is is it solid state?