You don't have the 'master' keyword for your NTP commands either. Therefore your switch is not likely to be providing NTP but only receiving NTP.
'ntp server' is to configure the switch on where it gets its NTP from.
'ntp peer' might work though whe...
That works! You don't even have to assign the L3 interface an IP, just enter "no switchport" to one of the two looped interfaces. It is a shame you have to burn two interfaces on a single switch just to keep the management VLAN interface up.
