Due to its unique effect of switching into Defense Mode after it attacks, "Submarineroid" would be a good card to combine with "Morphtronic Map". Keep it safe from attacks, and you have both offensive Life Points attacking and the gaining of Morph Counters.
Have a face-up "Final Attack Orders" with any of the above cards to change the Battle Position of all monsters on the field twice in one shot (once for a card like "No Entry!!" and again when "Final Attack Orders" forces all monsters back into Attack Position).
"Set Rotation" can also be used to Set "Morphtronic Map" to the opponent's side of the field, from where it can be destroyed without decreasing its owner's card advantage.
The effect of "Ancient Fairy Dragon" can be used to destroy the controller's "Morphtronic Map", allowing them to gain 1000 Life Points and Special Summon a "Morphtronic" monster. However, if the player was to add a Field Spell Card to their hand by the effect of "Ancient Fairy Dragon", they would not be able to Summon the "Morphtronic" as they would have missing the timing.
Use multiple "Labyrinth of Nightmare" to generate Morph Counters every turn, a potential 3 counters per turn (at maximum).