Clive Cussler books feature DOXA dive watches. 

Unfortunately Jack Heuer wasn't able to add anything to the story, as the Lemania movement wasn't used by Heuer until after Jack was pushed out of the company in 1982 - so he couldn't comment on it. However, the information from TAG Heuer Heritage is that the watch is most likely made between 1982-1985 created by a supplier or watchmaker to what end no-one is sure, but in the context of the chaotic turmoil of the Swill watch industry and the supply chain during the "quartz crises" suppliers were changed quickly and under Piaget (from 1982-1989)many elements of production and creation were outsourced to save costs.  From this point we can say that many watches were produced with the Heuer name but most likely outside of the strict control of the brand. So it is not a serially produced watch under the control of Heuer or a known prototype piece commissioned by the brand. The Lemania 1341 movement in place is correct for the Lemania case reference 9801-72. Most likely the dial is Singer (maker of Rolex Daytona dial) or a similar quality dial maker created the dial as it has a number of elements from other brands. Next move will be to contact Breguet to see if they have any Lemania records to track down the serial number 3507003 which is the correct range for Lemania. The stamp on the rotor has been added similar to other pieces as quiet a few original stamps were with suppliers like Lemania. 

So, looks as if I may never know why it has a Heuer dial...

Hi John. Tough trying to get in touch with him. I contacted Marco Gabella who recently did an interview with Jack Heuer for Watchonista to see if he would act as a conduit to get a message. So fingers crossed. I used to be unsure whether it was legit or not, but you put it into perspective nd something I forgot, It wasn't made by Heuer but by Lemania for Heuer - that gives the correct context.  Now to prove it. Also found these as other examples of Lemania branding for other watch companies and promotors. 

Hey, thanks, John. I will get onto it straight away. I'll let you know.  

Any luck, John? 

The case and movement correct but my only concern would be the dial and hands. Look way too good 🙃. I suspect a redial at some point, but who cares. If you like it and it sings to you buy and enjoy! More💪to you. 

Every experienced Swiss watchmaker who has seen it also believes it to be legit. I have a photo of how it looked prior to the restoration from the 1980s. A couple of things were changed as my friend who did the restoration changed it slightly to his own likes. The inner tachy bezel was black and the base plate is an Omega 1041 rhodium (not sure why he changed that) but I have the parts. Everything else is original.