I think you're fine with the LP50s, just make sure you fill them to 3600 so you get your money's worth.
As far as the hose thing, I don't recommend your approach. The whole point of the reg around your neck is that a panicked diver is most likely to just pull the reg out of your mouth, not patiently ask you for your octo, or try and search your body to find it--in recreational diving there is no standard.
So, the panicked diver pulls your primary out of your mouth, and it's on a 20" hose. That means the panicked diver, probably also flailing and grabbing at things, is going to be right on top of you. 20" is basically no distance. And then, you're going to have to pull the necklace reg up to your mouth, and hope it doesn't fall out of that flimsy holder you have it in.
Alternatively, you could have your backup reg around your neck in a bungee/surgical tubing (that's what I use because it's softer), and your primary in your mouth on a longer hose that allows you to put a little distance between yourself and the flailing, panicked diver that pulls it right out of your mouth--and maybe kicks off your mask for good measure.
If you think a 7' hose is too long, get a shorter one. The 5' hose, looped under the armpit and around the neck once is the most common for open water. You only need 7' if you need to go single file through a passage.