ISP modem/router, how do I enable Bridged Mode and use my own router?

Bridging the connection is entirely dependent on your ISP, when your Arris modem reaches out to the DHCP server, it locks to your modem MAC address.

you are asking the Arris modem/router to become in essence a Layer-2 device (referring to the OSI layers). it's questionable whether or not your Cable modem is striping the source mac address and replacing it with its own on the way out to the ISP side. if your other router has an option in the WAN settings to Clone a MAC-address, you can try to mimic the Arris routers WAN MAC-address with the settings you were trying.

another option is to call your ISP and ask them to release your DHCP Lease. which will make the network have to relearn what MAC is associated with your Account.

the third option, if all else fails.

use the DMZ option from the Arris to forward all traffic to the WAN address of your second Router (essentially bypassing the double NAT Scenario).

The reason your ISP Doesn't want you using "non-Approved" Modems is because they use the firmware of the modem they give you to restrict, or (CAP) your bandwidth to whatever rate you are paying for.

The second reason is when you do not pay your bill, they can put your modem into a "Wall-garden" state, and the mac address of your WAN will be filtered/redirected & take you to a Captive Portal instead of the requested DNS look ups.

EDIT: if your modem is losing all settings during power loss, this isn't normal behavior. those settings are stored in non-volatile RAM. i.e power loss should have no effect on them. if it is essentially factory resetting every time its rebooted, you should have your ISP replace it ASAP.