There's no reason why the fiber needs to go via a media converter. As long as you have compatible SFPs, just use the SFP ports on the switches for your interconnections.
Leveraging the Stackwise capability is certainly a good idea. You'll need to plan your stack and re-provision the switches accordingly.
As far as your VLAN connections, there's no need to use physically separate lines for VLAN 20 and 21 as you have indicated on your "LAN new" diagram. I'd just trunk the interswitch connections and allow all VLANs over the trunks. You could even bond the two links together into a portchannel interface then for higher bandwidth.
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