Jay I would love to know more about this myself.  I discovered the other day mold growing in a damp spot on the back of the icebox where a cushion rests against it.  This is where the cold plate attaches to the inner wall of the ice box.  It looks like quite a project to remove the icebox unit from the cabinetry.  I have been lead to believe that moister build up in the foam causes it to deteriorate, and over time reduce it's insulation properties.  One suggestion was to drill holes in the ice box unit, and inject expanding foam...this did not seem realistic, or appropriate.  I would love to hear other ideas.  

Having just re-insulated my icebox for the exact reasons you note (soggy insulation resulting in high duty compressor cycling and condensation on the outside walls) I can attest the job is indeed 'quite a project'. Not really that hard, just somewhat time-consuming, disruptive and messy.

If your insulation is original then after 35 years or so more than likely it is completely shot. In my case it looked to be simple 'expando-foam in a can', sprayed onto the icebox.  Once I removed the icebox it literally fell off in soggy, wet chunks.

I knew re-insulating the icebox properly would be a big job. Trying to avoid the disruption I examined many, many different alternatives including 'by-passing' the whole thing and installing a 12/110v Engel drop in. Not a viable solution for me because while nice, the Engel is either a refrigerator or freezer, not both.

After literally years of contemplation and talking to refrigeration experts I never could come up with a easy solution. Finally accepting there were no shortcuts I just finally bit the bullet, ripped it all out and started from scratch. Once the icebox tub was out I was able to re-gelcoat the tub inside & out, fabricated forms around it and poured 2 part closed cell foam to form a solid structure around the icebox tub.

In the end it was totally worth it. I now have ice cold drinks and the compressor runs about 25% of the time saving me tons of battery life.

Thanks for the insight, Mike.  Jay, I can't see any other way to manage this issue.  Over time the insulation will continue to deteriorate.   If you come up w/another way, I would love to know!