I had this issue and here is the real answer in it's simplest form:
The switch is not hanging, it is simply no longer on the IP address you are configuring it from.
When configuring the switch using the default management IP address on VLAN 1, as soon as you add another IP, the default is disabled, meaning 192.168.1.254 is no longer configured. Before doing anything else, you should add a VLAN 1 interface using an alternate IP address first (even in the same subnet), then after you click apply, re-point your browser to the new IP. From there you can add all other IPs to your VLANs without issue.
More details and steps taken from another post:
When you are configuring layer 3 routing on a sg300 or 500 switch, once the switch is in l3 mode You need to:
1- give each vlan interface a static IP starting with vlan1. This can be the same as the default 192.168.1.254, but I recommend picking another address in case you decide to add another switch in the future.
2- Before setting an IP on the new vlan, assign an access port to the new vlan (so you can move your workstation to that vlan) for management if needed. vlan management --> port vlan membership. Once you assign the ip address, and your management interface goes away, move your pc to the port on the new vlan, give it a static, and reconnect to the new IP address.
3- use the console cable and CLI to configure the vlan interface, as the console port does not go down, or loose connectivity when configuring vlans.
