Here's where the difference comes in between a cover letter and a letter of intent. With a cover letter, you likely already have a solid idea of what the job opportunity is, and how to position yourself for it. With a letter of intent, you have to make a slightly trickier balance—positioning yourself as qualified for a job that may not be clear yet. To do that, align your self talk around the company or the industry, making sure to highlight your skills and achievements that would make you a good fit for the company. You can also be specific about your level and experience. For example, you should make it clear that you're looking for a manager-level position if you don't want to be considered for more junior or entry-level roles.
Go with one of the classics, because they're used for a reason. If you sound too stiff and formal, it comes off like a holiday card. If you reiterate your call to action, it can carry a whiff of desperation. Just get out gracefully and quickly once you've said your piece.