switch – Directing single subnet traffic via multiple VLANs

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I have a setup where I would like to distribute devices connected to a L3 switch in multiple VLANs but I have a DHCP server offering a single subnet to the switch.
I’m attaching a network diagram below for reference:

I’ve tried to set up with different VLANs but the limitation on my side is that the DHCP offers only only one subnet.
Switch is a L3 switch: 3750G
The reason behind looking for the VLAN segmentation is to reduce broadcast traffic and I’d appreciate any ideas to explore here.