Does This Sound Doable? My Only Hope (O/O SFR purchase)

[Joy Runzel]

I have to buy a house. 

FICO is 625, but only due to utilization (65%).  No derogatories. Cc debt is $15K.

Soon to be ex and I have agreed to sell our house. The only encumbrance is a $45K HELOC.

My realtor sent comps over yesterday; we are in a strong seller’s market.  The suggested listing price is $297,400. I am basing my thoughts on a conservative prospective sale price of $280K.

The plan is to pay off the ccs with the cash from the sale. I expect my FICO to bounce right back up in 30 days or so, yes?  Our escrows are typically 45 days.

One huge problem is income.  Due to a neuropathic disorder, I was down for the past three years. I literally *just* started an online teaching job as a 1099 IC.  I also get a small soc sec check ($720).

Yesterday, I got even more bad news. Apparently, though my student loans ($382K) are current and on income based repayment; the lender has to use 1% of the fully amortized amount to calculate DTI.

So much for ever buying another house again in this lifetime.

After having a lot of doors slammed in my face, a local lender proposed the following scenario:

Use $125K from the sale as a DP on a $175K house and finance $50K.

Is this possible?  Math is definitely not my jam. 

Questions:

Wouldn’t the lack of two years of income still be a problem?

What about the student loan issue?

What kind of interest rate would be likely?

Thank you!