Just to be clear on a couple of points.
TV360 is a completely different TV platform to V6 and is fundamentally not TiVo. Sky Sports remains fully supported on the V6, and the HD multi-screen (used on Sky Tennis thus far) is being developed for the V6.
SkySports+, whatever additional functionality that provides, will be on TV360-only at launch, but has not been ruled out for V6 subsequently.
When you request a conversion from V6 > TV360, you'll receive the new remote within a few days. You should then have short time to instigate the migration yourself before it's forced. Make a note of all your series links, they will get wiped as part of the reformat process - as will all recordings.