I see what you are saying re position of cheek/eye. If you look at most HFTers stocks the cheek piece is adjustable and set to around level with the barrel so it's a cheek rest and not a chin rest.
Take a look at an old Daystate Huntsman Bullpup done by B&M ...
The cheekpiece is slightly higher than the barrel. The buttpad on that can be lowered so you can rest it on the ground for HFT prone ... or you could set it high so it will sit properly in the shoulder. The intermount on that is high as it was designed for FT. That mount could probably be made lower so the scope sat at virtually normal height and you'd still be able to line your eye up. That wood is heavy and the rifle is quite heavy in general. The weight sits further back and is very stable kneeling and standing. The deep fore end is perfect for resting on a gloved hand HFT low prone and also for kneelers and standers ... and is depth legal.
I'm convinced that could be used for HFT ( as is ... but especially if that intermount was lowered a tad ) and a decent shooter would do well with it.