Southeast Michigan tenant 2 months past due (advice please)

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I'm facing a situation where a tenant has not paid rent and is now past due 2 months. I'm wondering how I should proceed... this is the first issue that I've had with a tenant (we only have 3 properties).

Here are the highlights:
- The tenant is on a month to month lease
- She's not paid rent for August or September ($1245 total past due including late fees)
- We've had the property going on three months, she's a carry over tenant and has had a poor track record thus far (but in Michigan we are legally obligated to continue the previous owners lease as it follows the property - not the owner).
- I've talked with her and she's been between "I don't care about the past due rent" and "I'll give you every paycheck to get caught up"
- I've filled out form dc100a (demand for possession - 7 day notice) and plan to mail that to the tenant tomorrow

IF this is not resolved in the next 2 weeks I'm considering going to court (I plan to use an attorney for that process)!

I understand every case is unique, I'm just looking for a run down on what others would do in this situation... the tenant is between jobs, very few resources, I'm not sure she could get caught up in a reasonable amount of time and I'd (generally speaking) like her out of the property.

My options as I see them:
- file the dc100a with the court and work through the process with an attorney
- don't renew her lease and wait another 30 days before (most likely) going to court to have her removed
- try to work with her in which case it's a terribly tense situation where neither of us would be comfortable

Thanks in advance,
Mitch