It's not clear exactly what the problem is, or what you need to achieve. Is there an address conflict between your SXT and this home AP?

I've not done so myself but I think you can create the configuration you described by adding a virtual wireless interface with a separate SSID. Remove this interface from the bridge, and assign an IP address and DHCP configuration. I think it would have to be a separate subnet, so make sure all your routing and firewall rules are happy with this.

If there's no IP conflict at the subnet level, you could configure your SXT with DHCP, but create static reservations for your devices. Or just give these devices static IP addresses. There's no problem with a LAN having both static and DHCP issued addresses in service, that's in fact normal. Ideal set your DHCP pool so it doesn't overlap with the static addresses, but it should avoid those conflicts anyway.