First of all, I can understand your point about the biopsy, but really, a 3.5 centimeter target isn't as big as it sounds. It's big in your neck, but not when you are aiming a needle at it. One sample is normal, especially when they see the fluid that comes out looks like they got a good sample (ie. not blood or fluid that's too clear).
A second opinion is a good idea, since you're getting some vague and conflicting test results. I would find a good ENT (not an endo) and take your records there. Personally, I did a similar back-and-fourth thing getting ultrasounds and biopsies. The ultrasounds showed growth over the course of three tests and the biopsies were inconclusive. Unfortunately, the biopsies are not terribly accurate. There are significant rates of false-positives, false-negatives, and "inconclusive" results. Many people (including myself) never get a clear diagnosis of cancer before they go in for surgery. It's more of an odds thing that you and your doctor need to discuss. Mine was growing and there were "suspicious" cells, so I had the surgery and it was cancer. Some people play those same odds and find out that it's not cancer, so they keep the second half of their thyroid and chalk it up to being cautious.
Also note that thyroid cancer rarely presents with any symptoms other than the growth. All my thyroid tests came out completely normal and I felt fine.
If you were on the central coast of California, I could recommend a great ENT surgeon, but I don't know anyone in Texas, sorry. I've heard it can be done with a very small incision, but it depends on where yours is and how hard it is to get at the nodule. After having the same 3inch incision open in my neck twice, you can barely see it now. It's on the neck crease, so it blends in. In other words, if it has to be done, you shouldn't have much scaring as long as you keep it out of the sun and keep it moisturized.
If you need more information, there are a lot of us on here who have been through this stuff, so feel free to post again. Good luck with everything. Let us know how things turn out.