I am establishing a single-employee company for myself (probably an LLC, but maybe an S- or C-corp). Can I establish it in a locality or state other than where I live and work, to benefit from better small business health insurance rates? Can I do it with a sole proprietorship?

No. You need to either have a principal business address within the state where you're purchasing coverage or have an eligible common-law employee with a primary work-site within the state where you're purchasing coverage. This common-law employee must be on payroll (not including a business owner or sole proprietor, or their spouses on the payroll). We don't believe you can just have them on payroll for one month or utilize a corporate mailing address as you suggest.