If the application was filed with the court of appeals, the rules of the court of appeals, along with any local rule for the district in which your case is would apply. Consult an Ohio appellate attorney to find out if a late application is barred.
The Ohio Supreme Court is fairly strict with the rules of procedure and their deadlines. Practicing the Ohio Supreme Court is not for new amateurs. If you don't have an attorney, consult with one.
On another note, motions for reconsideration are rarely granted -- even if they are timely filed by an experienced attorney.
Yes, it means that, although the court of appeals itself is divested of jurisdiction to rule on an untimely motion for reconsideration, in the court of appeals, because there is no "for good cause shown" or similar extension language in App.R.26.
A lawyer can help you find additional case law authority, if any exists, but I believe the rule is clear on its face. Therefore, the only court you need be concerned with at this point is the Ohio Supreme Court.