If given a block clearance from ATC - eg FL360-FL400 how are you managing the vertical flight profile / FMC in order to optimise fuel burn? Specifically B777, but, of course, interested in all the heavy types.
Please - no theorising, conjecture etc - just the established / effective SOPs that work for your airline.
Since no one has an SOP for that kind of a climb you probably won't get an answer. If issued that clearance most would maintain cruise speed and merely set climb power. I know this doesn't fit your criteria but it isn't something pilots are concerned about.
When the FMC says to climb, you climb. FMC doesn't have the functionality of very gradual climb (as far as I know). Maybe you can play around with the step climbs (ours is usual RVSM) and set 100ft for the step climb (if it works?). Next flight I'll give it a try on the FMC.
I've seen "closely monitored V/S 500fpm" (100-200-300 to start, in reverse to level off) but that is only for passenger comfort, and of course cruise climb of 2000ft.
VNAV sets full climb power for a 1000' level change. Not a fan of it but it's SOP on my current a/c.
Regarding step climb when given a block? Do whatever you want. I typically let it get a couple of hundred (200-300') below OPT ALT, then climb a couple of hundred of feet above OPT (200-300'), until reaching the top of block altitude.
For the Bus is quite simple. You either follow the Cruise Climb Optimum Altitude table in your QRH (FPE-CCL - Inflight Performance), which gives you the optimum altitudes according to your actual weight (also based on actual Mach Nș and ISA dev), or simply use the Prog page on FMGC and follow the Optimum Alt.
I always prefer to wait until 200/300' feet below Optimum Alt and then make a small step of climb until reaching the new Optimum Alt. Repeat until reaching the top of block altitude.
With a block altitude clearance, what you COULD do is to follow the FMC recommended level as it changes by 100ft. Once it recommends 100ft above, you could set the MCP 100ft higher, press the MCP Alt switch to set the new cruise level, and climb.
By doing so, you will remain in VNAV, and because the change in level is only 100ft, the aircraft remains "captured" and so the engines don't go up full power.
777-300ER/200LR, when the opt climbs by 100ft, its reset the ALT in the MCP, press the knob....and hey presto you get about a 300fpm climb still in VNAV PTH and very little thrust lever movement, am told it saves on average50KG-75KG or thereabouts an hour FWIW.