Upload speed for "away from home" streaming via fire TV beta TiVo app

I've been watching shows recorded on my Roamio Plus while away from home using Fire TV via the beta TiVo app. Both my TiVo and FireTV are hard wired via ethernet. My resulting streaming picture resolution is standard definition at best. Ideally, I'd like to stream HD, but unsure if it's even possible. What's the fastest upload speed that the Roamio plus can support? The internet service for my TiVo supports up to 10 mbps upload. The internet service where my Fire TV is located supports...

Upload speed for "away from home" streaming via fire TV beta TiVo app

Upload speed for "away from home" streaming via fire TV beta TiVo app