Discover in house fraud protection has worked well for me. I do wish they had better 2FA options. I also posted how I handled the security settings in discover. I am phone centric, but I only check my emails at specific times, no notifications.
My risk level seems low to hand over, more information to a third party. I just unfroze my credit to apply for couple major credit cards. I have a window to do some work and then I am freezing my credit. My point is you can probably reduce your risk negating the need for more protection.