I regularly cook beef the way you describe. I commonly make thick ribeye steaks, about 2-3cm, and put them, salted, directly on an aluminium baking sheet in the oven set to 55˚C. Then I leave them for about 30-60 minutes until it is time for dinner. At 55˚C they are piping hot, red and bloody, and juicy and delicious with the connective issue all gelatinous. The fat becomes soft and translucent but is not rendered. I sear them 30 seconds per side in a heavy and hot pan, before serving. My wife occasionally wants it more well done and will put her piece back in the warm pan.
Now we will get to the problem with the "big piece" - I assume you mean 2-5kg, a 2-4 bone rib roast. At a 55-60˚C oven the inside is not going to heat to 50 until the outside surface has been warm for dangerously too long. All the exterior surfaces of this roast will be coated in bacteria (like everything is) and there is a limited time you can hold these warm temperatures.
As a result, when I do a big thick piece, I start with a hotter oven (120-150C?) and turn the temperature down to about 65-70 when the meat goes in. Allow the outer surface to brown, sterilizing the exterior. I then monitor with an internal probe until the roast is done (for me, 60-63˚C).
So, the barbecue step in this case serves no function anymore. It probably won't be exposed to the smoke for long enough to impart any flavor.
Note: when you cook beef this way it does not need to "rest". If you let it sit out it will simply get cold.