In the book "Military Aircraft Visual Encyclopedia" By Jim Winchester says the HE-177:
Had a ceiling of 7,000m (22,000+ feet)
Top Speed 295 MpH
Bomb Load of 6,000kg (13,000+lbs)
Defencive guns x3 7.92mm, x4 13mm, x2 20mm
Perhaps in one of the hybrids, but not the H-6/H-10 variants. The H-6/H-10 would be a more logical choice, at least imo, because of the numbers produced and the abilities of the aircraft.
From what I remember, the version that carried the 6000 lbs of ord needed RATO's to get off the ground (I'm thinking someone somewhere got their "lbs" mixed up with their "kg", there is no way the He111 could lift off with 13,000 lbs of ord let alone have enough room to carry it all).
Also, keep in mind when their is a source saying X aircraft had a speed of Y, don't forget to check the weight in which it was measured. There is a difference in an aircraft that is loaded down with %100 fuel and full ords vs one that is %50 fuel and no ords. Some data does not differentiate and that tidbit is not disclosed. Food for thought.
I'm sure someone with a legit source will chime in on what the maximum speed of the He111 was at X weight and Y altitude.