I just checked out your website......what a great-looking truck! I always did like the look of the streamliner tankers. I am sorry I don't have any information on those Heil bodied trucks. I just thought I would share a photo of an old Texaco tanker truck I have, and help keep your posting on this site alive.
Mine is a 1937 International tuck. I purchased it in February from a friend in Arizona, where this truck was in service its entire life. It came from Holts Texaco in Gila-Bend, AZ. The body was built by Advance Auto Body Works in Los Angeles. It is amazing to me how Texaco was really into having their trucks as fancy as they could be. It is hard to tell in the photo, but there was a lot of chrome on this truck, and you can still see original pinstriping all over the cab and tank.....and even the wheels. I would say, though, the pinnacle for Texaco was with the streamlined design like your truck and the airflows.
Please keep us in the oldgas community updated on your great restoration project!