If you want some more yield, the best is to put some of it on an index fund, with the associated risks, of course, but since this is money that probably will not be used more than once every 5-10 years, I think that's OK. Just 20% on a stock index and 80% in savings account should give you enough security + some room for a possibly better yield. Or maybe 50-50 as was advised by someone else. Well, that's not really "emergency-fund" like, now. Hmm, maybe the problem is you have too much aside just for emergencies. Just keep some of it as pure cash for very urgent and likely emergencies (you will very probably meet a 3000$ emergency in the next 5 years, but you only MIGHT meet one than needs 10k), and invest the remaining sum in an easy to liquidate asset (i.e., stocks in a taxable account can be sold in a matter of minutes, that is way better than real estate).
As for all of those (including MMM) advising using debt (HELOC, credit card & others) as an emergency fund... It doesn't stop surprising me. Debt is really the american way of life, even the most frugal people in that country seem to use it as an everyday tool. Lost your main source of income ? No problem, man ! Just borrow some money to your future self and everything will be all right :)