Well, you calculated it! I'm saying I don't agree the calculation takes all factors fully into account.
I'm more than happy to consider
your calculations.
To get the same heat output through the floor for the length of time you want it, the heat of the slab is going to have to be increased to compensate. I don't see how your calculations factor in the additional losses from the slab to the sub-floor temperature as a result of the a higher differential for a longer time. The calculations need to be over an extended period of time rather than on losses in an instant of time.
This is a red herring. In the limit, if you heated up once from cold and left the system running forever, any additional time required would average out to zero. If you want to factor in additional heat up time, then you'll have to say how often you're proposing to switch the system on and off from cold. Then you'll also have to factor in a contribution to additional cool-down time. To be honest that's a waste of time in a broad brushstroke calculation. (If you want to propose your own numbers I can easily factor them into the calculation, but in the mean time I'm sticking to my own experience of running one of these systems for a decade, which is that additional heat-up and cool-down time are roughly equal).
We can take an alternative approach to the calculation, and still get the same results. British standards mandate a maximum total loss through a floor, including all perimeters/cold bridging at 0.25 W/m²K (you can read them [broken link removed]). That's a ten percent loss for a 100W/m²K system running at 40 K above ground temperature. The Kingspan numbers I gave are between 0.1 and 0.2 W/m²K (you'd
expect them to be better than the absolute limit specified in the regulations). The increased temperature for wood flooring is between 4 and 9 degrees in all the literature I have looked at (again feel free to provide your own numbers). That is between one tenth and one quarter of the temperature difference between UFH and ground, and since U-values are linear in temperature, means an additional 10% to 25% losses. Since the maximum losses are already 10%, that gives an additional 1% to 2.5% losses for wood, and the better end of the Kingspan range is only 40% of that (0.1 vs. 0.25 W/m²K), equating to 0.4% to 1% losses. It seems to me you would need some extraordinary parameters to hike that up to something non-negligible but, as I said, feel free to provide your own numbers.
The thermal resistance of the glue isn't factored in anywhere either, assuming the floor is glued to the slab. Membranes such as Elastilion will have a higher thermal resistance. Elastilions test results show their product just falling within the German guidelines for maximum thermal resistance when testing with a laminated floor panel to a combined thickness of 11.65mm (0.14 (MsqK)/W versus the max of .015).
The figures I gave for the wooden flooring
include a soundproofing and moisture barrier layer for a floating installation as well as the boards themselves, which happens to be the sort of system I'm running. Having seen the sheeting go down during construction and being suprised at its thickness I very much doubt it is less insulating than a layer of glue in a fixed installation. You can check the U-values in the link I provided.
There's a reason manufactures recommend UFH pipes are laid more densely where wooden floors are specified.
None of the ones I checked do.
Another point not considered for the OP is whether the rest of the insulation and air-tightness detail is sufficient that the reduced effective 70W/square metre will meet the heat requirements for the room.
Not relevant to the efficiency calculation though.