Has anyone created a lease that made all parties jointly responsible, but allowed one to stay for, say, 6 months, and after the 6 months, the tenants staying for 12 months become the only responsible parties? 

Lets add in the improvements.....Adding $10k per unit would be $30k and your return on investment for the improvements made will most likely be too low for it to make financial sense.

I have been hesitant to rent out my current home because we've spent the last 5 years remodeling and improving the home to such a degree that, with it being in "move-in ready condition", I would be worried about how renters would take care of it from here on out. 

Turns out she didn't completely chase me off with a shotgun or anything, but she did tell me that if her situation doesn't improve, she'll definitely be calling me to discuss more details.

But probably not if you don't think it would improve the property.

I have taken great strides in improving my credit recently, and have also looked into what it will cost to start up a LLC.

Keep a good part of your focus on the rent you can achieve with the improvements you're making.

Are they jointly and severally responsible for the lease? 

I would do it as long as the income is right and stable and she seems like she wants to improve , maybe a additional deposit 

Thanks @Wesley Williams for the intro@Jonathan Smith there's a lot you can do with just a little marketing.You could call the basement an "office" or a "den" and that's something you could market for higher rent.Also, I've written in detail about an "Inn Keeper" profit center where the landlord joint ventures with the tenant to host Airbnb/VRBO guests.