One of the player characters in a game I run is a halfling rogue. I want to give her a non-evil shadow mastiff as an intelligent mount due to synergy with her rogue features. This is a case where the Rule of Cool will bring my player some happiness and a unique edge, so I am not interested in being told I am wrong for trying this (even if I am). Rather, this question will be about a matter of balance.
The shadow mastiff has a feature called Shadow Blend, described as follows (Volo's Guide to Monsters p. 190):
Shadow Blend. While in dim light or darkness, the shadow mastiff can use a bonus action to become invisible, along with anything it is wearing or carrying. The invisibility lasts until the shadow mastiff uses a bonus action to end it or until the shadow mastiff attacks, is in bright light, or is incapacitated.
Since the rider does not count as a thing being worn or carried, the rider does not turn invisible with the shadow mastiff when it uses this feature (as affirmed by a related question). Therefore, using Shadow Blend as written leads to the case where a rider mounted on a shadow mastiff stays visible while its mount becomes invisible, and that strikes me as silly and immersion-breaking. Let's call that the "invisible jet" effect after the appearance of Wonder Woman's invisible jet.
How can I effectively avoid the "invisible jet" effect when a shadow mastiff is being used as a mount?
I am looking for a GS/BS answer describing a house-rule that modifies the text or interpretation of the Shadow Blend feature just enough to avoid the "invisible jet" effect.
However, it needs to have been tested at a table in similar circumstances (relating to any sort of invisible mounts, not necessarily to shadow mastiffs in particular) and confirmed to be balanced and effective by reasonable metrics.