I suspect Hull-Barton-Brigg even without serving Barnetby would be at or very slightly over an hour each way, so couldn't be done with 2 vehicles on an hourly frequency, or if it could be done, there would be no recovery time. The 'shorts' had 42 minutes between leaving Barton Market Place en-route to the airport and returning. Barton to Brigg and back non-stop in 42 minutes, yes, but add in hopefully some stops for passengers and any waits at traffic lights in Brigg, and 42 minutes seems like being far too close for comfort.
Hull to Cleethorpes is timed at 1 hour 52 minutes and Cleethorpes to Hull at 2 hours, so no time to divert to Barnetby on all journeys without either an extra vehicle being used or a frequency cut. When Barnetby was served once a day it took advantage of peak time variations. The morning service was the vehicle from the peak time journey into Grimsby that didn't extend to Cleethorpes, and then started 'short' from Grimsby to return to Hull. This 'short working' created some slack in the timetable so the Grimsby to Hull 'short' could leave Grimsby earlier and serve Barnetby before getting back onto 'standard pattern' at Barton. The afternoon service from Hull that went via Barnetby had a longer turnaround on arrival at Cleethorpes due to the slightly over an hour gap mid-afternoon in Cleethorpes departures; this time was used to serve Barnetby. This 'slack' was reintroduced into the timetable when Barnetby was dropped from the service.
and consequetly
was the first off peak service that starts short from Grimsby, and consequently ran 10 minutes earlier
and the afternoon service took advantage of the slightly over an hour gap from Cleethorpes later afternoon
The Brigg Line Group have published an alternative proposal for a regular service from Cleethorpes to Worksop.
http://nigelfishersbriggblog.blogspot.com/2020/06/new-shuttle-trains-could-serve-brigg.html?m=0
North Lincolnshire Council have submitted a bid for goverment money to conduct a feasibility study into the NNLCRP scheme.
The North Lincs Council / North Notts and Lincolnshire Community Rail Partnership bid for funding for the feasibility study into extending the Sheffield - Gainsborough Central service through to Barton has been successful.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/938907/restoring-your-railway-successful-bids.csv/preview