I have been approved for a term life insurance policy with a A++ rated
company but not at the best health class so my payments would be
higher that if they had placed me in the best health class.  If I
decline to accept this offer and apply with another insurance carrier
that I think may evaluate me with a better health class, will the fact
I have declined the first policy negatively affect my chances of
getting the best quote from other insurance companies.

Not necessarily.  Insurance co's are eager for your business.  You may
see some variance of offers among co's, as some underwrite certain
conditions differently.  However, if you were rated for a common
condition (i.e. diabetes, HPB, etc.) I wouldn't expect a dramatic
change in the rate at another company.  Also, you may have been rated
simply because the underwriter didn't have enough information to make
a better offer.  The more complete medical records you can provide,
the better chance you have of getting a fair offer.