Up to you Don.
It's your choice.
One tactic could be for those that have a parent or birthplace abroad to register under that country, and then if they do make their host team decide then? If they don't make the team then they can elect to shoot for their other country/ies.
You're not alone Don. I've counted 5 shooters who could qualify for England and could also by these rules shoot for other countries. It allows us to pick from an even wider field of shooters due to residency, yet those who don't make the team can just elect to shoot for their home nation and still get to attend. The EFTA could effectively cherry pick with internal rules, leaving those without a team place the option of what they wish to do.