So you have a TiVo & a V6. Before asking for a TV360, please be clear on the implications.
TiVo refers to both the software (that both your boxes currently run) and the older ("wider" you call it) box. TV360 is completely different - in a similar way to Android being different to Apple.
If your TiVo is faulty, as very much sounds, it will be replaced with a V6 as a matter of course and you will have two identical boxes on the same basis as your main box is now. Both have their own hard drives, both can record but can also multi-room stream.
TV360 is a completely different TV platform, and cannot co-exist with TiVo/V6. Meaning you'll need to software convert your existing V6 into a TV360 (reformat, lose all your recordings and start with brand new software), and your TiVo will be replaced with a TV360-mini box that won't have its own hard drive and will be reliant on the master box for all recordings.