You'll be fine. I wouldn't hesitate to tow with that truck. 108k is not all that much. I towed cross country with a '95 'Burb that had 126k on it when I left for the trip.
Regarding the heads, do some research. As already said, if it was a problem, it would have been long ago.
For the trans, you say it was well maintained? I'd still get it checked out if you don't know what you are looking for yourself. If the trans was properly maintained and not over heated it will last forever. Do you have maintenance records? Fluid/filter should have been changed every 50k. Change it anyway and use Dex VI, not Dex III. If you are handy, do it yourself. Dex VI is full synthetic, is backward compatible, and the trans will run much cooler. My old '03 Trailblazer has the same trans (4L60E) with 160k on it and its as strong as ever. The trick is to keep them from over heating. I used Dex VI and didn't allow it drop gears at the drop of a hat.
On the subject of replacing the hitch, there were a few threads here some years back where a couple of members had some issues with failed hitches. These were all 2002 and an investigation was issued by the NHTSA. (
PE07025). As far as I have ever been able to determine only 4 complaints were ever actually made about this. And if it was an issue, you know the guy at dangeroustrailer.org would have been all over it. Its not even mentioned on his site.