With all due respect category 6 patch cables do not effect the performance of your ethernet home network in the way you describe.
The only time a home user may need category 6 patch cables is when they are actually using category terminated wiring (permanent wiring installed in the walls/dwelling) AND then only if you are running gigabit ethernet. Category 6 has nothing to do with the quality of the HD signal transmitted across the ethernet network, but rather the speed capabilities of the ethernet network. the majority of ethernet devices in a typical residential home is limited to a maximum of 100 Mb and using more expensive ethernet cables will not change that.
You are are also confused about the MoCA 1.1 standard used by TiVo devices, the maximum data rate is 175mbps with a maximum physical throughput of 275mbps. The throughput you describe is the MoCA 2.0 standard which the best of my knowledge, despite its approval, no manufacturer has yet to market. Yes, MoCA 2.0 which as you describe offers 800 mbps in enhanced mode (400 in standard mode) however Tivo products at the this time only support the slower MoCA 1.1, the newer MoCA standard will support the older 1.1 however it will then slow all devices down to the 1.1 mode which in a sense defeats upgrading until all your devices can support MoCA 2.0.
Yes cat 6 or cat 5e cables are recommended if you are connecting two Gb ethernet interfaces however, I have yet to see standard cat 5 cables work for 1gb ethernet or even 10gb ethernet (I Btw maintain enterprise data infrastructures for a living and more working experience with high capacity data networks than most third party support engineers do).
I scoff at the crazy prices that box stores charge for these cat 6 "high speed" cables, to the average home consumer, this nothing more than nutty, misleading marketing! If you need good cables a good source is www.cable2go.com
Do not buy the plastic wrapped cables that Bestbuy sells for $25+, that's just nuts!
Furthermore, it is technically impossible for any TiVo device to exceed the theoretical limits of a 100 Mb switched connection despite the Plus & Pro Roamio's having a 1gb ethenet enterface. If I were to speculate the only reason those models have them is for future support of MoCA 2.0 should any products supporting that reach the consumer market. You do understand there is a big difference between the descriptors suffice of "mps", "mb" and 1gb when referencing throughput and speed of a interface esp relating to ethenet? You can not easily compare the three in relationship to actual operating thoughputs.
There are no absolutes when it comes to MoCA networking esp when can be so many other factors involved especially when a MoCA gateway is connected to an existing home network. Maximum theoretical throughput numbers are a pie in the sky limit that few if any networked devices can actually achieve.