I experimented a lot with these last summer. They really hit the front delts and triceps harder than normal overhead presses, because you can't really flare your shoulders out to bring the whole shoulder into play.
Some things to think about--they are not an easily grooved lift; even doing them often I found it hard to 'practice' them. If you're after pure brute strength increases this is a good thing. Also, they don't have a ton of carryover to normal (pronated grip) strict presses, at least not by themselves. They build a ton of strength at the sticking points at both the start and middle of the lift. So, after getting back to normal OHPs when I practiced them for a while I felt like I had fewer limiting factors at those sticking points.
Other stuff--you can't press back behind your head obviously, if you have to grind it out leaning back slightly is probably the way to go. Pushing your head through the hole/pressing up and back just can't be done here unless you have incredibly flexible shoulders.
You don't have to worry about dropping the bar on your head. I'd say start out trying a slightly wider grip than you usually would on strict presses. I think that pavel's recommendation for 'elbow friendly barbell curls' in 'beyond bodybuilding' applies to grip width here. Also, try to spread the bar across your palm, not just a straight up supinated grip but push your wrists back so that the bar can rest on the meaty spot on the base of your palm; same as a kettlebell. Keep the weight there and you won't have to worry about dropping it.
One final thing--I have tiny wrists and normal strict presses sometimes don't feel so great. Reverse grips do not give me any sort of wrist trouble. Also, I could be wrong but the underhand grip may help you get your lats more into play at the bottom if you've been having trouble with that.
I'd say primarily use it as an assistance exercise for any sort of strict overhead pressing (bb/db/kb/odd object) you might do, especially if you don't do horizontal press variants.
I'm not an amazing presser nor do I have a ton of experience with these, but a few months of hard work helped me get up to the 'bodyweight press' barrier for the second time, and very slightly past it for the first time.