The default route forwarding ip is nothing more than your default gateway for the switch. Your hosts will have the ip of the vlan be their default gateway, and for whatever your switch doesn't know about it will send to it's default gateway. Generally, you'll want to default gateway on your switch to point to your egress device (firewall, router, etc.)
It looks like you're doing a lot of static routing though. Is this for this example, or have you been adding routes directly to your workstations? I would just recommend setting the default gateway on your workstations to point to their respective vlans.
On your ASA, your switch will need to have a route to point to the other side:
ip route 172.16.0.0 255.255.0.0 10.192.0.253
And then your ASA, if you're not running ospf, eigrp, or rip between the ASA and switch, will need to have a route to the switch for subnets that the ASA don't see as locally connected:
route inside 10.193.0.0 255.255.254.0 10.192.0.1 (assuming .1 is your switch)
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