Routing outside the 6248

Alright, I know this is a basic question and I've done a bunch of looking around and hours worth of trying different configurations with this 6248. Here's what I'm faced with:

• I have a flat network at this point that is 192.168.1.0 /24.
• I have a cable gateway modem at 192.168.1.1 that I use to get northbound to the Internet which is NOT capable of setting static routes.
• DNS is a VM at 192.168.1.5.
• My 6248 has several VLANs, all of which I want to route between:  1, 5, 6, etc.
• I want from every VLAN to be able to get internet access through the said cable gateway.
• VLAN 1 is 192.168.1.0 /24 network.
• Switch interface for VLAN 1 is 192.168.1.25
• Switch interface for VLANs 5 and 6 are the .1 of their respective networks, so 192.168.5.1, etc.
• Switch management interface is on VLAN 250 with IP of 192.168.250.250 /24
• All existing and future VLANs will be simple /24 networks.
• Nothing is plugged into this 6248 right now while I get the configuration right, aside from an uplink cable (access port) into the 192.168.1.0 /24 network, and a test connection to an ESXi host where I'm testing different VLAN connectivity through a VM port group.

And now, questions/problems:

1. Since on this switch you cannot route between the management interface VLAN, I had to create this on VLAN 250. So right now, I can't connect to the management interface, but I can connect to the interface at 192.168.1.25. Given my network right now, how/where should I configure this switch management interface? Or is it fine like it is?
   
   
2. Because my cable modem gateway is at 192.168.1.1, if I'm testing connectivity from VLANs 5 or 6, while I can reach everything on VLAN 1 (including those hosts not directly connected to the 6248), I cannot go northbound to the internet. I have also put a default route in the switch for 192.168.1.1, but that isn't working. If I am connected to the 6248, configure a port group on VLAN 1, and set the gateway on a test VM to point to 192.168.1.25, I can get out to the internet. I can also ping the router interfaces for VLANs 5 and 6.

Here is my config:

!Current Configuration:

!System Description "PowerConnect 6248, 3.3.14.2, VxWorks 6.5"

!System Software Version 3.3.14.2

!Cut-through mode is configured as disabled

!

configure

vlan database

vlan 5-6,250

vlan routing 1 1

vlan routing 5 2

vlan routing 6 3

exit

stack

member 1 2

exit

ip address 192.168.250.250 255.255.255.0

ip address vlan 250

ip routing

ip route 0.0.0.0 0.0.0.0 192.168.1.1

interface vlan 1

routing              

ip address 192.168.1.25 255.255.255.0

exit

interface vlan 5

name "test"

routing

ip address 192.168.5.1 255.255.255.0

exit

interface vlan 6

name "test"

routing

ip address 192.168.6.1 255.255.255.0

exit

username "admin" password db32549314c1390177c34647bf960343 level 15 encrypted

!

interface ethernet 1/g25

spanning-tree portfast

switchport mode trunk

switchport trunk allowed vlan add 1,5-6

exit

exit