You maybe able to break into the 600's but there is no way that you will magically jump past the 600's into the 700's. I would pay off your four small debts to free up more disposable income.
You can get up in the 600s and the best way to do it is like this:
1. Immediately pay off your outstanding balances.
2. As soon as they are paid off, dispute the accounts with all three credit reporting agencies.
Here is why...
Once the balance is paid off, a lot of collection agencies will not want to bother responding to your dispute. If they don't respond within 30 days, the reporting agencies must take them off your credit report immediately.
That means that they will not show up as a past collection and paid. It means that there is a good chance that they will disappear for good, which will increase your credit score dramatically.
You might get to 600 by January, but no way you'll get to 700 by then.