There are actually quite a few options, many of which come naturally when you're not forced to consciously write formally.
You can change the verb into an –ing:
"Having done freelance for 8 years, I..."
"Choosing to work from home has..."
or in some cases turn the verb into the subject or your sentence.
"Experience with Java has helped..."
This gives it an assertive feel, as does any other form of eliminating personal pronouns. Though one should include some personal pronouns for fear one begins to sound impersonal. :)
You can also add introductory phrases or prepositional phrases to the beginnings of your sentences:
"In my extensive set of skills, I..."
"With my passion for social media, ..."
If you're currently writing the cover letter, it might be best to get all your thoughts and strengths down first before editing for repetition and word choice.