I think the key point here is holding a constant N1 (fan rpm).
As you accelerate in forward speed, your increasing airspeed is ramming air into the fan/compressor, and that "helps" them to spin (think of a pinwheel in a breeze), requiring less effort from the power section, so N2 probably rolls back a bit to hold a constant N1, producing less thrust at the exhaust.
If your throttle control was holding a constant N2 - then you'd get approximately constant thrust, but your N1 would climb towards redline as you increased airspeed.
As to a thrust decrease in climb, that is a normal function of getting into thinner air: less air to push (thrust) and less air to burn (to do the pushing). Even at just 3000 feet, you are in ~8% thinner air than at sea level, with a corresponding decrease in engine output.
(That may be - in Terry Pratchett's words, "A description that is wonderfully illustrative, while being, in every technical detail, completely wrong!" )