MAJOR UPDATE - TOYOTA WARRANTY EXTENSION FOR "STICKY DASHBOARDS"
Today ( 12/29/2014 ) I received in the mail a Warranty Enhancement Notification regarding my Toyota. Complete coincidence that I received this a few weeks after I posted the original question.
A relevant December 18th, 2014 article from a consumer investigator regarding this issue.
Important excerpts from my Warranty Enhancement Notification include:
This program will extend the warranty coverage for repairs related to cracked and/or sticky/melting Dashboards (Instrument Panels) as a result of heat or humidity on 2003-2005 model 4Runner, 2005-2010 model year Avalon, 2007-2011 model year Camry and Camry Hybrid, 2004-2010 model year Sienna, and 2004-2008 model year Solara vehicles.
Dashboards can become cracked and/or sticky/melted over time for a number of different reasons and under a number of different circumstances. If the Dashboard has become cracked and/or sticky/melted as a result of heat or humidity, the repair will be performed at no charge as soon as parts become available.
Primary Coverage offers warranty enhancement described herein for all owners until May 31, 2017, regardless of mileage or date of first use of the vehicle.
Secondary Coverage supplements the Primary Coverage for some owners by offering the warranty enhancement described herein for 10 years from the date of first use of the vehicle, regardless of mileage.
... coverage is for warranty work performed for the covered Dashboards and must be performed at an authorized Toyota dealer only.
If you have previously paid for repairs to address any {qualifying} Dashboard, mail a copy of repair order, proof-of-payment, and proof-of-ownership to address for reimbursement consideration:
Toyota Motor Sales, USA, Inc.
Toyota Customer Experience, WC 10
19001 South Western Avenue
Torrance, CA 90509
Original, December 17th, answer follows
I discovered the following during research after I posted the question.
Searching online against "Toyota Camry Sticky Dashboard" returns many very specific results, including videos. There are many reports of Toyota Camry vehicles (standard, hybrid, and other variants) from the 2007-2009 year range producing a sticky dashboard, which eventually transforms into a shiny, reflective surface, which creates a definite driving safety hazard, obstructing the driver's view.
Per Hawaii News Now, Toyota's stance is the original warranty only. As this tackiness of the dashboard seems to happen more often after 3 years, once the warranty has ended, and since there is no recall program, many owners are out of luck.
What can a consumer do? Concerned U.S. consumers can file a complaint with the National Highway Traffic Safety Administration (NHTSA) with an emphasis on (1) the stickyness of the dashboard, and (2) the shiny/reflective surface the dashboard creates, as a safety hazard. Reviewing the NHTSA complaints reveals multiple submissions regarding this specific issue; perhaps if there are more submitted, the NHTSA will investigate and prompt a recall.
Otherwise, I cannot recommend how to repair the surface.
Feb. 19, 2016 UPDATE: Of note, I have been on a waiting list to have this repaired for over a year; my local dealer claims that Toyota has not yet shipped any replacement dashboards, but I find this hard to believe.
April 2016 UPDATE: One year and four months after getting the warranty extension, my local dealer finally received dashboards and replaced mine. It looks fine now; no issues, no stickiness. Now if only they'd address the poor leather stitching, the degrading ceiling fabric, the disintegrating steering wheel, and the interior black paint chipping off the power window buttons. I'm never buying a Toyota again.
January 2017 UPDATE: They replaced the cracking dashboard of my wife's Solara convertible, which was also under the recall. Unlike my dashboard, hers has a very funky smell, as though someone had smoked several packs of cigarettes around it. The dealership assured us this is normal and will fade over time.