As I recall it the "Longhaul Agreement" didn't actually stop the use of Long haul types/crews being used on Short haul routes, and it doesn't generally demand crewing of such by management pilots..but it can generate cost issues.
Over the years I've operated the 747/744 and the T7 very very occasionally from London (both LHR and LGW) to the likes of Manchester and also Paris on day trips, but those only due to "force majeur". The Manchesters were down to lack of short haul airframes/crews and the Paris trips were associated with ATC strikes leading to slot and flow restrictions and the solution was to consolidate multiple narrow body services into one or two widebody flights.
OTOH in relatively recent years there was a long standing LHR-MAD-LHR day trip on the T7 fleet ( I think the 787 Fleet inherited it), and also the aforementioned DME on the 747 or the T7...those were very much pre-planned and published a month or more ahead of the operating dates in the appropriate bidpacks/bidinfo and therefore available for the line community to bid for.... or bid to avoid..
The "quirk" the long haul agreement
did however throw up was (sometimes?) there was a requirement for the company to provide accommodation at base pre/post duty, can't remember the details..that not only quite understandably generates
within the short haul community it also costs the company money so I suspect that's where any alleviation might come into play.