I would suggest giving a completly seperate IP address range.
the ip address and mask tells the device/pc if the device it is trying to get to is on the same network as its self.
lets imagen this
PC A is on your origianl net work.
10.3.37.87/22 Default gate way 10.3.36.1
PC B on your subnet
10.3.39.10 255.255.255.224 Defualt gateway 10.3.39.1
ok now PC B sends a packet to pc A's ip address (lets say a ping)
PC B looks at its ip address and subnet mask and can work out that PC A is on a different network. so send the packet to the Default gateway (DFGW) this will be a router and if the routing is set up correctly send it to the PC A network.
now the reply packet.. PC A looks at its IP addres ITS SUBNET MASK and PC B ip address. It sees PC B as being on the same network as its self. so will try to contact it directly with out sending the packet to the DFGW! as PC B is on a seperate VLAN it will not be able to communicate with it and the packet has no way of getting ot its destination!!!
REmber when a PC is looking to send out a packet. it looks at its own IP and Subnet mask and ONLY the IP of the destination system. (it dosent know the destination system mask)
Now with a lot of fiddeling around you can get this set up to work. however much better would be to chose a second ip address range.
why not chose a 192.168.x.x/24 range for you test network/vlan.
you have exactly the same problem I have had in the past. splitting up a large network in to chunks. you need to add new address ranges rather than split the current range you have, it will be much simpler. and means that you can keep all the rest of the PC's on the old network exactly as they are now same subnet same DFGW, create new ip ranges and migrate PC's over as you go.
each vlan on you core router has an ipaddress assigend to it from its ip address range for the ddevices to use as there default gate way.
IF you want it a bit clearer let me know and I will pull out dsome digrams.
Also get hold of packet tracer from cisco to test it out on (its a nice network/router simulator)