Anyone with a calculator can tell the numbers don't add up. You're either embellishing or you got scammed.
It's kind of a silly fight, and I'm sure it would help educate a lot of people reading about what is possible.
Then choose r'/r < 1/2 by a sufficient amount. For example: let (P; r; t) be ($100,000; 8%; 30 years). The payment is around $740/mo. Now take (P; r; t) equal to ($100,000; 3%; 15 years). The payment is around $700/mo.
You can adjust for the fact that some months of repayment already occurred so the term reduction is to a new term greater than half the remaining periods on the existing loan and the present value (i.e. new principle) is smaller and bump r' up accordingly to achieve the same result.
Either way it's hardly "impossible" and actually quite easy to do if there's a significant difference between the original loan conditions and the refinance/consolidation.
https://www.wolframalpha.com/input/?i=$100000+3%25+15+year+m...
https://www.wolframalpha.com/input/?i=$100000+8%25+30+year+m...
Again, the specific numbers of your situation would go a long way to shutting up the skeptics here. Either your initial rate was absurdly high, or you're exaggerating.
my knowledge of finance
... apparently does not include knowing that "principle" and principal have different meanings.