In 2008, overnight rates rose because firms didn’t trust their counterparties or their collateral. In this case, rates are being driven up by a lack of supply - banks have to hold more reserves post-crisis, other firms were making tax payments. There will likely be a shortage again at the end of this month when a bunch of Treasuries expire.
And, if I do look for something else, the long term rates are, in many cases, no more than the short term rates. So I have renewed 90 days CDs and little else.