Personally, if I'd had dino oil changes every 3,000 miles, I'd see no need to do anything other than to make the switch. Just be sure to use a good filter (I like Pure One by Purolator and Mobil 1, though many are fine). I believe you have the maintenance minder (MM) feature on your '06. If you do, I'd follow its guidance and change when it says. MM takes data from the engine control computer, including temperature and cumulative RPMs, to figure out how much oil life has been used up. Seems to be the way manufacturers are going.
If you don't have MM, you can probably stretch it to 7500 miles.
I have one car with MM and I am changing it when it says with synthetic. My other family cars have synthetic and I change them every 5,000 miles ALONG WITH THE FILTER. It seems like overkill, but I just sat down and figured it out , and my family has driven 1.2 million miles on synthetic with this regimen without an oil-related engine failure. That includes two cars that went past 200,000 miles, two past 150,000, and four past 100,000 miles. Some of those cars were well used when we acquired them, including a 1993 Volvo 940 Turbo Wagon that had 73,000 when we bought it and is still blowing strong at 224,000 miles. <sound of fist knocking on wood>
Hope this helps.
If you don't mind, I'm curious as to how you've racked up 36,000 miles on an '06 on an island about the size of Vermont.