If I were you, I would not route the traffic through both the ASA and the RV340. Both devices have similar feature sets (in your scenario), and using both would be redundant. Since you already have dual-WAN setup on the RV340, and since you just want to use the ASA for VPN, then just put the ASA off to the side.
In the above drawing, the RV340 is the default gateway for all vlans (represented by colors). The ASA is on its own vlan, but it could be on a common vlan with something else, too. In your RV340, add a static route for the far-side of the VPN tunnel, pointing at the ASA.
For configuring DHCP on the RV340, scroll to page 55 of Cisco's documentation for the RV340.
Page 41 of the documentation talks about Policy-Based Routing, which is what you use to get certain vlans to use a certain ISP.
One final comment: if your ASA were newer, then you could do policy-based routing on it, also. In that case, I would not use the RV340 at all, and would do everything using the ASA only.