Hi William,
You’re not going crazy! 
The term “Half Dead Beat” is used for two totally different escapements. The one that you ask about where the entry pallet is used for locking only and impulse given only on exit is also referred to as a half dead beat. These are not seen too often. The much more common half dead beat where impulse is given on both entry and exit pallets is the one that you have and is seen on many American clocks. Some people feel that the term should only be used on the one that has impulse on exit only to avoid confusion but that to me seems like it would just cause more confusion as I think most of us in the U.S. relate the term to the type that you have. So whether correct or not I’ll call it a half dead beat and will just continue to dodge bullets from those who feel I’m wrong.
You may be right about spanning 8 teeth William or at least moving the pallets a little further apart to allow for a little more drop and lock. The most agreed upon number for obtaining maximum efficiency for a “dead beat” with an escape wheel of around 30 teeth is 7 1/2 teeth (I think) and it looks like your clock may have around 40 teeth so I would think that a span of 8 1/2 teeth would be quite possible. If it is meant to be 7 1/2 teeth then changing it to 8 1/2 would decrease the pendulum arc as the distance from the escape wheel center to the verge pivot center would need to be increased. So I think the answer to your question “can you have a verge span 7 teeth and get the same results if you span the same clock 8 teeth?” is… almost. If the same clock is changed from 7 to 8 and maximum efficiency is maintain by adjusting the escape wheel to anchor center distances and pallet lift angles to get as close as possible to the max efficiency of 50% then the pendulum swing arc will be smaller. In practice 50% isn’t possible as a little bit of fudging needs to be done to get enough drop and lock for the escapement to function properly but you can get close.
I’ve got to run into town for a bit and will take a look at LaBounty’s description when I get back. I think if you are following the standard way of checking to see if the pallet angles are correct (I think that’s what he was showing) then yes I believe you are right on target.
I’ll be back home in a couple of hours or so and will check it out better. I just fired this stuff off so please don’t take what I’ve posted above as fact until I can verify it by going through some books etc. when I get back as I’m going from memory which usually isn’t too accurate! At this point it’s just some food for thought.
Back in a while,
Bob