Rosebud, did you finally get the chance to go over all of this with your doctor, and was she able to explain it to you in a way you could believe? I really don't think you need to spend the money on testing, and if you were to remember that doctors go to school for many years and are trained in this kind of stuff, it might help you ease your mind more than more lab tests anyway. I know docs are busy and are limited to short time periods with their patients, but was she able to help?
I vote for your ex. Your late period in August could have been caused by the turmoil of your break-up or travel schedule. A normal 31 day cycle starting Aug 21 would have lead to ovulation Sep 5th which is when you were active with the ex. Your 15 week ultrasound is likely accurate to days, not weeks. Your due date will be around the end of May. Good luck!
"Implantation bleeding" is mostly an Internet myth, spread in posts by women who are scared that their (multi-day) menstrual flow was not a period. But an embryo is smaller than the dot on the letter i in this sentence, and when it embeds in the uterine lining, if there is any reaction at all, it is not going to be days of bleeding. More like a little wisp of blood one time in your vaginal mucus, or nothing.
Discuss the situation again with your doctor, telling her that you want to be sure of when you might have conceived, and use the word "conception" or "conceived," not "how far along am I" or other more vague terms. She should be able to walk you through why you can believe all the ultrasound evidence of the size of the baby.
At 15 weeks, the US is still pretty accurate. For it to be an entire month off, and your baby being a month older than 15 weeks at the time of the US is unusual. Also, your fertility window could coincide with a Sept. 3-7 time frame.