I'm not exactly sure why this worked for me, but what I ended up doing was to modify my web.config like so:
<membership defaultProvider="DefaultMembershipProvider"
hashAlgorithmType="HMACSHA256">
and
<machineKey
validationKey="50E5BFCB171748F86DA392AC55D5217EDEFCE43C9B6D192C5265D8F0CDDC86CECBA42040C408B7B71EAD6A4CE669545AAFDE76BBA42CA44203223A7ADC442D1E"
decryptionKey="EE9C03B1D922639AB7BA3C00E8C993BD8F6D27635B07979DF09F8C174C91CA65"
validation="MD5" decryption="Auto" />
The existing membership info seems to be allowing me to sign in now.