What lens/reflector when bouncing off ceiling
I'd like to "fill" a room with ambient "daylight"


Well, ambient daylight can be over 1 kW per square metre so 15x 10 watt LEDs (at 30% light conversion efficiency) is about 50 watts. However, The World Meteorological Organization regards 120 watts per square meter as the minumim to count as "sunshine" so this helps a bit but how far you go down the scale towards 120 watts per sq metre is your call.

Also, in a room that could be filled with normal daylight to the standard you hope to achieve maybe it would need (estimate) 6 square metres of windows. That would be 6 x 120 watts or 720 watts and remember this is the bottom end of the Meteorological Organization's limit. 

So maybe a kW through 6 sq metres would be OK. Take a look at this graph: -



A lot of the incident light power is made up from infra red so, if you do some more research you can estimate the equivalent visible light power. Maybe it's about 50% of the 1 kW so possibly 500 watts of light diffused into the room would give the impression of being lit from real sunshine.

Of course the LEDs are only about 30% efficient so you will need an input power of about 1500 watts. You are quite possibly a long way short of the overall power needed to give the impression of daylight.