Cisco WAN :: SG500-24 - Switches Between Cable Modem And Router?

Currently, my Cisco DPC3010 cable modem is connected directly to one of the Ethernet ports on my Linux router.  All works quite well that way.  However, I'm curious to know if there's some what to separate the router and cable modem over 2 switches?
 
The coax enters the house in my living room and connects to the CM there.  The router is also sitting in the living room, and it's connected to a Cisco SG200-18 switch.  I have Ethernet running from my living room to my basement, where a Cisco SG500-24 switch sits.  The two switches are connected via a 2xGigE port channel.
 
I want to move the router into the basement.  Ideally, I'd like to move the CM down there with it, but I don't have the necessary coax run.  So for now, that's out.  But... can I go from something like this:
 
--coax----- Cable Modem ---GigE----- Router ---GigE---- SG200-18 ===2xGigE==== SG500-24
 
To something like this:
 
--coax----- Cable Modem ---GigE-----  SG200-18 ===2xGigE==== SG500-24 ---GigE----- Router
 
I tried it, complete with a separate VLAN specifically for the CM traffic.  And the VLAN was properly trunked between the two switches.   But for some reason, the router was unable to communicate via IP to the upstream.  I'm not sure if there are config bits I need to set on the SG200 that the CM is connected to?  I thought I'd read somewhere that CMs don't like broadcast technology such as LLDP and/or CDP, so I disabled both of those on its port.  Did I miss something else perhaps?  Or am I trying to do the impossible?
 
For what it's worth: the IP connectivity is static.  There's no DHCP running between my router and the upstream cable provider.  The cable modem is literally acting as a L2 coax-->Ethernet convertor, more or less.