First off, lets me just start out by pointing out what I think you SHOULD have done when you got divorced: Contact Sallie Mae providing the information for said $7,000.00 loan as well as the property settlement agreement detailing that YOU would be responsible for the loan. I have no way of knowing if your ex would have been difficult about this, but its certainly possible that the lender would have allowed you to sever that loan off of her account so that you could pay it off directly. It's also possible that they would have refused, but now it seems a little late. You could still try it, but I doubt Sallie Mae will even speak to you and your ex doesn't seem happy with you such that she'd be cooperative.
Given your current situation, is there any dispute about the remaining balance? Whether there is or not, if this were me I'd want something in writing from the ex confirming the exact amount that YOU still owe as well as any other terms that she expects you to abide by. Sure, she may be asking for $70 or principal only, but what's to stop her from later claiming thats just what you sent, even though it wasn't the full amount.
As far as proving the money is sent/received: Sure, you can send certified mail if you want to waste upwards of $5 every month....I'm thinking there are probably cheaper services available if you just want to prove the date it was sent and/or received. Then again, you can also just mail the checks and when they're cashed by your ex, well voila there is your proof that it was received. In fact, you could even use money orders if you don't want to deal with the money from your checking account being in limbo. You'd probably also be better off if you sent along some sort of note with each payment showing the date you're sending it, the amount enclosed, and the new balance and make sure that you keep photocopies of the letter. Later, if there's any question about the balance, you have got a nice stack of letters showing exactly how much was paid and how much was left during any given month.
You CAN try to get a loan for the entire amount and just pay her (if you do this you had better make sure you have good records of that payment) but if your credit really is as poor as you say, you're only going to end up with extra interest for yourself. The upside, I suppose, is that you'd be regularly paying off a loan (on time) and utilizing your credit in such a way that could theoretically improve your score.
For what its worth: I am a lawyer, but not where you live, and therefore I can't and won't give you "legal advice". The information here is merely what I would do in a similar circumstance based on common sense and life experiences. If you think you need legal advice, contact a lawyer who is admitted in the State where your divorce papers were filed.