Personally, I would mount them towards the drawers. Make sure to secure the radios in a sense, if they break contact with the charger they won't be charged when you need them, hence why a lot if flashlights (rechargable) clip into the charging base. This can be just a bump or something resting against the radios.
Would make one suggestion regarding your (correct) assessment of holding the radios in place.
I submit what has always struck me as a kludge solution but one that has worked fine for years with commercial radios.
The strap or tie-down being various things, sometimes barely more than a bungie cord. Point being if the cradle is reasonably secure it could be just as simple as adding a length of whatever elastic-type sort of thing.
Variations of this I've seen with Motorola and Kenwood, maybe others, for years. And it's used in tough situations, like cop cars and fire engines and lumber trucks.
Now slots like this and the charging interface is designed to be robust in the first place, so there's a fundamental leg-up over more delicate consumer stuff. But it surely can be adapted to work.