I understand your dilemma. Failure to report your positive payment history will artificially decrease your credit score. It is notable, however, that many credit providers do not furnish information to all three national credit reporting agencies (Equifax, Experian and Trans Union). So what appears on one report, may not appear on all.
The credit reporting agencies and credit providers have a duty to report "accurate" information about you on your consumer credit report. They do not have an obligation under federal law to report all information, however. If your lender indicated they report at the start of the month, it may be that they are reporting to a different credit bureau than the dealership where you subsequently tried to get approval for financing (presuming it was a dealership where you sought the credit check). Ask your lender who they report or furnish your information to. Perhaps the folks you are trying to obtain credit with now can pull that report instead.
Your obligations under the loan agreement with the lender are going to be based upon the loan agreement itself. Failure to report your account history to the credit bureaus, in my view, is not grounds to get out of the loan agreement.
Good luck to you!
NOTE: This Answer does not constitute legal advice. Every case is fact specific. To render a legal opinion, an attorney must engage in a consultation with a prospective client and review any pertinent documents. This communication does not create an attorney-client relationship with Attorney Amy L. Wells or WELLS LAW OFFICE, INC.