Turtle-- Several members have shared several different ideas. I am unwilling to comment on the merits of any of them, however, let's see if we can develop a gameplan for you to become a licensed PE.
I think that you will find that many states will require additional coursework if you fail the PE examination 3 or more times. I think that 3 failures requires you to demonstrate to the board that you took additional coursework in the specific discipline that you tested in to give you additional academic preparation for sitting for the examination. You are going to waste more time screwing around trying to find a "way out" of this then just taking the 12 hours plus whatever additional stem work you need for the 12 hours. I do not expect that the board will "forget" or "not see" that you did not have the additional 12 hours, especially since your original degree is NOT in civil engineering. So, point one is to take the stem work and then the 12 hours of additional work-- this may mean 18-24 additional hours of course work. However, by your own admission, you do not have a civil engineering degree, so you probably need the additional course work to have a greater understanding of the principles of the civil discipline, if that is where you elect to sit for the examination.
Point 2 is to review the examination specifications for the appropriate civil examinations to see where your background best fits. It may be that the examination section that you sat for was the best fit for your experience and academic preparation, but you were unable to "self teach" yourself the material needed to demonstrate minimal competency in the examination.
In my mind, there is no reason to continue to spend money and time trying to "force fit" something that probably requires additional preparation. When I moved to my current state of residence, I had to sit for the examination, even though I was currently registered in Texas, had been for many years, but because of graduate school degrees, did not have to sit for the PE exam in Texas. This was several years ago-- the rules have all changed and now, irregardless of degree, to include the PhD, you have to sit for the examination. In the end, it was far easier to take the test and pass it then continue to try and find away around the rules established. I do recall a colleague who appeared before the Texas Board of PE's to petition for an academic waiver (he was an adjunct professor) who owned a business. He was denied the academic waiver and one of the board members, a CPA pointed out that CPA's try the same thing, i.e., try and get a waiver instead of taking the test and demonstrating proficiency. My colleague has NOT, TO THIS DAY taken the PE examination in his discipline. I suspect that he will never do it-- even though he could probably pass if he put his mind toward it.
I do agree with previous commenters-- persistance is a wonderful trait and you should not give up on any of that. However, let's get the necessary preparation you require, take a good prep course, work 20000000 problems, take the exam one time and be done with it. I know, at this point, this looks very daunting. However, it is not as daunting as it appears. Get the course work you need, study the material they recommend you to take, take a review course, take the PE exam and be done with it. In the end, this is the best solution for you.
Good Luck.