How do I explain using aliases without giving the appearance of misconduct or impropriety? ... What reaction(s) should I expect from the company and HR personnel?
What you're asking is how to lie to a potential employer, tell them that you've lied and have them be okay with it. Don't expect the relationship to continue when they find out; this would be no different than any other lie.
Additionally, if you're bound by a contract that says you agree not to search for a new job, using an alias doesn't change the fact that it's you doing it, nor does it put you any less in breach of the contract. Using that as a justification for what you've done will also tell a potential employer that you don't take your commitments seriously. That won't end well, either.
Should you make it all the way through the process and receive an offer, consider what the says about the caliber of people the company hires.
Are there better strategies to make contact while protecting candidate privacy?
One would be to hire an agent to make first contact companies on your behalf. Your agent will be on the same footing as every other recruiter trying to place a candidate into that company and will have to get past the barrier of convincing the company that there are no strings attached. It will probably also disqualify you from any company that doesn't deal with third parties.
The other would be to dial back your stance and evaluate why employers use these companies, what their policies are with respect to how your information is handled and whether or not you believe they'll safeguard your name. I work for a company that uses a third party application service because they help us with otherwise-expensive regulatory compliance. That service lays out its privacy policies in detail on its web site, which gives you sufficient information to decide whether or not you want to interact with them. Your reaction may be "they say they won't disclose my information but they might," but there's also nothing that prevents an unscrupulous HR drone who received your resume directly from quietly selling the information they collect on the side.