Re: your first question of talking to a VP competitor, absolutely. You need to network where and when you can and keep all options open. Check the ACHE website and under Career Services, you will find the Career Management Network (Affiliates Only). You can access other ACHE members for networking. Also, see the Leadership Mentoring Network.
As far as the entry position, check out the article on the ACHE website under Career Services titled "Your Career as a Healthcare Executive" for some additional ideas. If you don't have direct supervisory experience, start to think about opportunites you now have or had in the past, where you led a project or team, as well as situations (on the job or off) where you displayed leadership qualities. Maximize these experiences on your resume. In addition, your HR experience makes you knowledgeable of basic management activities such as hiring, performance evaluation and training.
On your last question - shadowing, if you ask, the worst that could happen is for someone to say no. Set realistic time and expectation parameters and give it a try. Mike Broscio - ACHE Career Resource Center.