ITA with eyePod. I keep a larger EF because it helps me sleep at night.
It sounds like you are a lawyer, and that you have annual contracts. I know the legal field, and it changes extremely quickly, and when it crashes, it could take months to find a new job. IMO, I would not want to risk credit cards or stocks for money that I realistically might need within a couple of months, knowing that it might take me 6 mos. to find a new job. However, your annual contract gives you some ability to time things, so I would target everything around that contract renewal date. So for this year:
1. Take $10-15K of your cash, pay off the highest-interest loan, throw the rest at the next one.
2. Max out your 401(k) at $1500/mo. between now and the renewal date.
3. Throw all the monthly excess between now and then at the 6.2% loan.
This leaves you with 2.5-5 mos. in EF and at least half of a fully-funded 401(k) if you aren't renewed (size of EF should be related to your comfort zone/likelihood of renewal).
Once your contract is renewed, though, you know you don't need a big EF for another 364 days. So keep a little in cash and throw all the rest at the 6.2% loan. Continue to max the 401(k); divert $750-$1K of what's left to the EF (again depending on your risk tolerance), and then the remainder to the next-highest loan (adjust as necessary to cover minimums once IBR kicks in). Or you can front-load the loans and back-load the EF even more to minimize the amount of time you have cash just sitting there -- e.g., right after the contract is renewed, throw all the extra money back at the loans, and then a few months before your contract renewal date, reduce the loans to minimum payments and build the EF back up. In either event, by your next renewal date, you'll have a decent EF built up again and over half the loans gone. If your contract is renewed again, rinse and repeat.
Note: I'm a big fan of using the 401(k) while the getting is good -- not only is it use-it-or-lose-it, but it will decrease your taxes, so the $1500/mo hit is more like $1200 (as compared to the loan payoff, where $1500 is $1500).