Don't know if it is best to Refinance or do a Home Equity Line of Credit. 

Thats going to improve your chances.

We also bought during the first-time homebuyers credit era, so we got a check for 10% of the purchase price back with our taxes, and if I remember correctly, we used an FHA loan with 3.5% down.

I've got excellent credit at the moment and a job with six figure income (however much lower after taxes/student loans/primary mortgage), would this help gain what I want with a lender?

Sounds like you have added close to $100k of value, added $1,000 a month of tax smart cashflow to your bottom line, improved your personal quality of life, reduced your company's business expenses, and still have more upside.  

In our case improved operations provides the self-funding to make these investments possible, to the detriment of cash flow during the first 4-5 years, but we planned for that going in.  

When you work six days and take the seventh off, your physical, spiritual, emotional, mental and even your financial health will greatly improve – and so will your success rate.

During that time, I also had 2 mortgages that were successfully modified--but as a result my credit scores have suffered and dipped to the low 600's.

ITT students might be able to transfer their federal loan credits elsewhere or possibly have them canceled.

. $3400, maybe take out cash advance on my credit cards $2500, and do a cash out refinance to get the equity out of my house.