More Opportunities for Rural Economies from DOT Grants Act or the MORE DOT Grants Act This bill revises the process for awarding grants under certain programs of the Department of Transportation (DOT) to high-density public land counties and any units of tribal and local governments within such counties. A high-density public land county is a county that has a population of not more than 100,000 people and in which more than 50% of the land is owned or managed by the federal government. Any requirement for local matching funds under a qualifying grant program must be reduced by 50% with respect to such jurisdictions. On request, DOT must provide additional technical assistance to such jurisdictions during the annual application period for each qualifying grant program. DOT must also prioritize grant applications from such jurisdictions that have not received support under the qualifying grant program during the 10-year period preceding the date of the application.