Jeepers!
Leaving aside engine factors for the moment (about which I know little
), lowest fuel consumption occurs by definition at the speed for best L/D ratio, Vmd (min drag). This is commonly shown as a 'green dot' on FMS-equipped aircraft. This is also the speed for best endurance (another way of saying min fuel burn).
Slower than Vmd means more drag and therefore more fuel burn. Ditto faster.
It is therefore axiomatic that the most economical profile when required to lose time, all other factors being equal, is to reduce speed to meet the RTA as far as green dot. Any additional time required to be lost should be done in vectoring or holding at green dot.
Note: This assumes level flight and does not account for compressibility factors. In jet aircraft fuel burn typically increases at lower altitudes, but this is balanced by reduced TAS at green dot (i.e. the aircraft can go slower at green dot). Wind gradient is also a factor to consider. Therefore there is a balance between all these factors but I don't know enough detail to reach any authoritative conclusion as to the best vertical profile to fly, but the normal rule is stay as high as possible for as long as possible.