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I mean this kindly, but LW you are making a lot of excuses. Of course you can afford an internship. Everyone I know who gets paid to write started out writing for free to get clips.
If you really want this, you have to chart a course and follow it. And you have to accept that in the short term, you have to give some things up to get those clips, starting with your full-time admin job.
In my 20's I worked as a waitress, a line cook, an office temp and a part-time office assistant. The reason I took these jobs is they allowed me to work at a part-time unpaid internship, which was the only job furthering my actual career. Internships are like school, you need to work odd jobs to make them work.
Another thing: you claim you can't get hired to write due to lack of experience. So another option is to get a job copy editing, which you have experience doing. Then lobby for opportunities to write at that publication. Or get any kind of job for any kind of publication, and then beg and schmooze your way into writing.
I could go on with options, but I sense you'll resist them. Your letter makes it sound as if you are only open to the possibility of immediate work getting paid for writing despite your lack of experience. You need to clarify your priorities. There's no practical reason anyone would pay you to write without seeing clips.
You may consider asking yourself why you are only open to the least likely scenario. Are you sure you want to be a writer?