and it CAN, under certain circumstances, result in either a sole-source contract, OR at least give the submitting company an inside track for competitive business.

OK, fine, John, but what should we make sure is included in any such proposal?

Reality
First, "unsolicited" is not exactly correct. To be successful, these proposals must have or find a Champion within the customer for whom the offeror is actually creating the proposal (board member; technical guy; key advisor; key staff person; key senior executive), and it is for his use that we submit our materials. Therefore, it is usually best to submit a semi-finished version of the proposal to that individual, and then re-draft it before final submission. In addition, that is the time to get a "heads up" on what opposition to expect within the organization — and take steps to overcome that opposition. There may be known pockets of support or resistance outside the organization (for example, if the proposal is to Division A, there may be a critical member or members of Division B that must know about, and support, that proposal).

Be Careful
Before you do a lot of work toward preparing an unsolicited proposal, know your customer well enough to know that the customer will refrain from using YOUR work to award to someone else, even your worst competitor. For example, in the 1980s I was working for Aerospace Contractor "A“. Aerospace "B“ solicited a proposal from us on an aircraft program. We dutifully responded with our best ideas. The "customer“ thanked us for our work, handed the technical solution to another division within "B“, and awarded a contract to that division, with instructions to do the work as "A“ had suggested. Oops!

Five Major Headings
1. Executive Summary
2. Management Volume
3. Technical Volume
4. Cost Volume
5. (Proposed / Model / Draft) Contract

Elements of the Contract(You MUST have a thorough legal review before going out the first time)
Identification of parties
Authority to commit
Addresses
Statement of Work (SOW)
Type of contract
Relationship of parties
Duration of contract
Termination
Verification of deliveries and liquidation
Payment terms and methods
Conflicts of interest
Rights in data
Patent rights
Location of work
Agreements not to disclose proprietary data
Disputes
Interpretation of the contract

Summary
This isn’t meant to be all-inclusive, or to cover all possible situations, but it’s at least a good checklist to guide your thinking.