Let's say we're looking at a five-year trend. It doesn't matter what it is - let's say the number of students in a certain teacher's class.
The numbers are 25, 27, 23, 32, and 25 again.
If you say "as much as" you refer to the highest number. She has taught as many* as 32 students in her class at one time. That means that some of the numbers will be lower than 32. (That would be considered a very large class size where I live.)
On the other hand, let's say you come from a place where the classes are always overcrowded. You may marvel at the year she had only 23 student and say "She has taught with as few as 23 students in her class." You pick the lowest one.
It is entirely incorrect to suggest you can substitute "as many as" with "as few as" in a context like this.
*You can count them, so you say "many" not "much," but if it were a percentage, then you'd use "much" instead of "many."
However this is not the situation you describe.
Yes, we would say "no less than" to express surprise at a very high number. Exports have risen by - can you believe this number? listen to this - 80%! = Exports have risen by no less than 80%! It seems to require an exclamation mark, to indicate the expression of suprise.
You can't substitute "at least" here - the surprise factor won't work. (There's a thread here about "no less a person than the Dowager Empress" -- again meaning "Wow! It was a person as important as the Dowager Empress!")
And finally at least and "no less than." These can be neutral.
How long do you think the drive will be?
Plan on at least 2 hours. Plan on no less than 2 hours.
It will be no less tha 3 hours, but no more than 5, even if you hit the worst of the traffic.
EDIT: Oh, I see you have only "no less than" and that "no" is different from the "as" I described above. Oh well - you seem interested in these things, so maybe these examples will help in the long run, even if it wasn't your exact question.
Interested in Language