Things that "come into play tapped" should not fire triggers for Mode$Taps according to my reading of rule 603.2d. I hope I haven't missed any place where this might be happening.

src/main/java/forge/PlayerZone_ComesIntoPlay.java

@@ -46,7 +46,8 @@ public class PlayerZone_ComesIntoPlay extends DefaultPlayerZone {
                 || (AllZoneUtil.isCardInPlay("Root Maze") && (c.isLand() || c.isArtifact()))
                 || (AllZoneUtil.isCardInPlay("Orb of Dreams") && c.isPermanent())))
         {
-            c.tap();
+            //it enters the battlefield this way, and should not fire triggers
+            c.setTapped(true);
         }
 
         //cannot use addComesIntoPlayCommand - trigger might be set to false;

src/main/java/forge/card/cardFactory/CardFactoryUtil.java

@@ -4976,8 +4976,8 @@ public class CardFactoryUtil {
                 private static final long serialVersionUID = 203335252453049234L;
 
                 public void execute() {
-                    // System.out.println("Executing previous keyword");
+                    //it enters the battlefield this way, and should not fire triggers
-                    card.tap();
+                    card.setTapped(true);
                 }
             });
         } // if "Comes into play tapped."
@@ -4989,7 +4989,8 @@ public class CardFactoryUtil {
                     CardList lands = AllZoneUtil.getPlayerLandsInPlay(card.getController());
                     lands.remove(card);
                     if (!(lands.size() <= 2)) {
-                        card.tap();
+                        //it enters the battlefield this way, and should not fire triggers
+                        card.setTapped(true);
                     }
                 }
             });
@@ -5026,7 +5027,8 @@ public class CardFactoryUtil {
                     }
 
                     if (!fnd) {
-                        card.tap();
+                        //it enters the battlefield this way, and should not fire triggers
+                        card.setTapped(true);
                     }
                 }
             });

src/main/java/forge/card/cardFactory/CardFactory_Lands.java

@@ -63,7 +63,7 @@ class CardFactory_Lands {
                         AllZone.getComputerPlayer().loseLife(2, card);
                     }
                     else {
-                        card.tap();
+                        tapCard();
                     }
                 }
 
@@ -88,7 +88,8 @@ class CardFactory_Lands {
                 }//execute()
 
                 private void tapCard() {
-                    card.tap();
+                    //it enters the battlefield this way, and should not fire triggers
+                    card.setTapped(true);
                 }
             });
         }//*************** END ************ END **************************