The Application for Extracting and Exploring Analysis Ready Samples (AppEEARS) now has a selection of MODIS Version 6 products available. AppEEARS enables users to input precise sample locations and access analysis-ready data from tiled land MODIS products held by the LP DAAC.
Try AppEEARS for yourself: https://appeears.earthdatacloud.nasa.gov/
AppEEARS is considered Beta at this time. Feedback about AppEEARS can be sent through the interface: https://lpdaacsvc.cr.usgs.gov/appeears/feedback.