Custom OS isn’t going to address the anaemic hardware, nor do I think relying on open-source custom ROMs for a niche item is the best way to ensure any hardware-level vulnerabilities are covered.
If you already have an Internet-connected device hooked up to your TV (eg. PlayStation); there is no need to connect another, especially when it provides an overall worse experience.
Shit, a basic HTPC is infinitely better - using a Linux-based distribution (which will have a lot more support vs. a niche TV ROM), and it’ll be supported well beyond what the hardware could handle.
That sounds awful; hopefully you were at least able to poison their DB with a fake name and a 10minutemail (or similar) account?