1. Award a fixed pool of H1Bs to qualified applicants with the highest wage in the offer (and monitor that this wage is in fact being paid). This should be easy to pass if your representatives in congress are in fact _your_ representatives. The president will sign this immediately, since he was the one who proposed it in the first place.
2. Establish at least 6 month grace period if the H1B person leaves the sponsoring company to go work elsewhere. Currently if you leave (or are laid off/fired) you have to GTFO within 2 weeks, so people endure abuse and low wages for years until they get a green card.
There. There's your solution. No need to do anything else, guaranteed to work. It should not be possible to hire foreign workers into entry level positions at all.