My proposal to solve the problem of ships like the Type-7, which can fit in the area of the medium landing pad, but don't fit inside the dock due to their height, is to allow them to only dock externally, or rather not being given permission to enter the inner dock.
The game already has some considerations for such scenario: without entering the inner dock you actually have access to most of the features in the dock, from mission board, universal cartographics, refueling & restocking ammo, etc. The only exceptions are 3 services: shipyard, outfitting and livery, which do require going into the inner dock.
Therefore my solution is to allow these ships that can fit in the area of the landing pad to not have access to those 3 services, but otherwise allow them to use the other services that don't require internal docking.
For example: a Type-7 would be able to dock in the medium landing pad of an outpost and have access to most of its services, but even if the outpost can provide outfitting, livery and shipyard services to medium ships, these won't be available for large ships like the Type-7 which fit within the area of their landing pads. Needless to say, they also won't have the option to use the elevator and be moved into the inner dock.
In essence, the same could apply to medium ships that fit in the area of small landing pads, but are also too tall to fit in the internal dock, but I imagine that scenario to be of less concern given the larger availability of medium pads, thus mostly something that could be used if, for instance, all the medium landing pads of a freighter were taken, but a small landing pad was available.
The game already has some considerations for such scenario: without entering the inner dock you actually have access to most of the features in the dock, from mission board, universal cartographics, refueling & restocking ammo, etc. The only exceptions are 3 services: shipyard, outfitting and livery, which do require going into the inner dock.
Therefore my solution is to allow these ships that can fit in the area of the landing pad to not have access to those 3 services, but otherwise allow them to use the other services that don't require internal docking.
For example: a Type-7 would be able to dock in the medium landing pad of an outpost and have access to most of its services, but even if the outpost can provide outfitting, livery and shipyard services to medium ships, these won't be available for large ships like the Type-7 which fit within the area of their landing pads. Needless to say, they also won't have the option to use the elevator and be moved into the inner dock.
In essence, the same could apply to medium ships that fit in the area of small landing pads, but are also too tall to fit in the internal dock, but I imagine that scenario to be of less concern given the larger availability of medium pads, thus mostly something that could be used if, for instance, all the medium landing pads of a freighter were taken, but a small landing pad was available.
