LGB,
I think that you answered your own question within your question when you stated -
(disregarding loss of climb when accelerating and cleaning up)
That is the key item to be considered for any OVERALL gradient up to ther point where gradient no longer matters. The loss of gradient during acceleration to flap reduction speed is very significant - I always monitor Flight Path Angle on every departure, and (on the B777) the gradient routinely is as low as 1° (1.6%) or less. For a 4 engined aircraft, this will be even more limiting due to the considerably lower excess thrust with all engines operating.
I know of no aircraft where even low flap extensions produced a gradient better than in the clean configuration, and the clean configuration would undoubtedly yield an improved instantaneous gradient than would 10° Flap, the problem is the severe overall gradient loss during the acceleration to the better configuration and speed.
Regards,
Old Smokey