Part of the answer to your question has to do with an aspect of bonds and bond funds, called "duration".
For a single bond, you understand the time to maturity, the date the bond returns its principal and you have your initial investment back. But. Along the way, you get money from the semi-annual interest payments. Loosely speaking, you can think of duration as the time-weighted average to get your money back taking the payments into account.
A zero-coupon bond's duration is equal to its time to maturity. A bond with a high coupon will have a duration much lower than its maturity.
That said, the fund you cited has an average maturity of 8.2 years, and an average duration of 6.0 years. Why is this important? Duration tells us how the bond (or bond fund) reacts to changes in interest rates. A change of rates of .1% will cause a price change close to .6%. (In effect .1 * 6 is how that's calculated) Therefore, the extra yield you seek is traded for the extra risk in a way that's 100% quantifiable.
My goal is not to talk you out of doing this, only to help you understand one of the fundamental issues of investing, risk vs reward. Even the risk averse member who has money in FDIC insured banks as cash might have close to 100% 'safety' in theory, but still carries the risk of inflation, for example.
The second fund you cite is a total market index. Not suitable, in my opinion, for the emergency account. See other posts here for the emergency account discussion.