Dynastine scarabs are basically everywhere in the United States depending on the species. Dynastes grantii occur in Arizona abundantly, and rarely found in adjacent states. They fly around starting May-June to September to October, however the peak flight season is late August to early September. Its sister species, the D. tityus can be found from eastern Texas west to Georgia north to somewhere near New York. I know there are records in lots of counties in Philadelphia. Try go to Philadelphia in sometime June to July as it is closer than southern states from your location, Maine. Strategus are here and there. Strategus aloeus is considered very common species in Louisiana, and its peak season for adults is from late June to early July in Louisiana. Its sister species, S. antaeus, that is less common can be found from last week of May to first week of June in Louisiana. Somewhere in North or South Carolina has records of Dorcus parallelus as well. It is very small Lucanid beetle, however, is one of the Dorcus species. Lucanus elaphus should be available in Virginia and around. Refer to Bugguide and/or iNaturalist records to see when and where the records been made in your area or nearer area to your state.