The other option he had for direct transport through the wards was a type of transport he called "flaming". It was something he had done once by accident, escaping a hellfire attack from a demon summoned by Voldemort. Afterward he had learned to control it much the same way he apparated.
This approach completely bypassed the apparition wards. Indeed they had never found wards that would prevent it. Despite the tactical advantage being able to get through wards like that offered, the Hermione of his world could never figure out how exactly he was doing it or how to teach others to do it.
Ron had once told her, "It's just one of those Harry things." Hermione had huffed, offended, but had eventually conceded when she couldn't find a better explanation; especially since when she asked Harry how he did it, his response was a blank stare and a "I just wanted to, and did…" His lack of technical awareness, and ability to make magic do what he wanted despite not following preconceived "rules", could drive Hermione spare sometimes.
It had further irritated her when an entire afternoon was spent with Harry flaming from one side of a room over and over with the hope that Hermione could figure things out. At one point Harry had gotten bored and wondered if he could change the color of the flames just to mix it up. On the next jump he had changed the flames to green, and then blue, and then purple.
Again when Hermione asked him how he was doing it, he told her with a shrug "I was bored with red." Harry couldn't explain how to do it, much less how to change flame color.
However the downside to flame travel was that it was flashy. As he appeared and disappeared in a pillar of flame. Just appearing in the middle of a group of wizards in a flaming pillar was unlikely to help him keep a low profile; and since he couldn't explain his presence on this world, keeping a low profile was paramount.
So, after picking himself up off the ground and the undignified sprawl he had ended up in, Harry had walked toward the stadium, to the large grouping of tents outside that were currently empty. He was still feeling odd as he moved, being unused to a body that was whole and functioning. He had only made it a half mile before he caught the comforting sight of his familiar in the sky above him. He couldn't stop the sad smile on his face at the intelligence and protectiveness of his loyal familiar even after all this time.
He continued to walk and could feel the magic of the huge muggle-repelling wards, and notice-me-not charms as he passed through them. He also felt various other wards tied in, though he couldn't be sure what each individual ward did without taking time to examine them. However, Harry was relieved that no one was around because he did feel that one of the wards he walked through removed his glamour spell. Rather than drawing any attention to himself by recasting the glamour, he pulled up his grey hood so it obscured his face.
Harry arrived in the area around the stadium just as wizards and witches alike streamed from the stadium. Apparently the game had just ended and the champion's had been crowned. It didn't take him long to overhear that the game and score was the same as it had been back in "his world." 170-160 with an Ireland victory. Bulgaria's Ivanova had scored their only goal, and Viktor Krum had caught the snitch.
Harry stalked through the huge ensemble of wizards who were all lost in their merriment or their griping about the results of the World Cup. Currently he was in the midst of some Bulgarians who were all bemoaning the fact that their team, with the exception of their seeker, had been roundly eviscerated. Some were angry and raging at the officiating and the loss of their beloved team.
Harry's own mood matched that of the people around him, but for a far different reason.
He had made his little side trip right before coming out here to the location of what seemed like every witch and wizard in existence. He had apparated to the town of Little Hangleton. He brought himself right to the edge of the rundown shack that was the former house of Gaunt. It was absolutely unchanged in this world.
Harry's idea had been to take the ring that had been one of the Horcruxes in his old world, before Dumbledore got cursed by it in this world. His plan was rendered worthless almost immediately. Harry was cautious on approach to the shack. He took his time and cast every detection spell he ever learned, as well as stretching his senses out to try and feel any magic. Other than some very old and faded traces of magic, the shack had nothing. No ring. No Horcrux.
Harry was fuming. Either Voldemort had hidden the ring someplace else, or he had never used it as a Horcrux.
That made Harry wonder what other changes occurred in this timeline that he wouldn't be prepared for. It was more than enough to put him in a foul mood. Harry was tempted to burn the building to the ground in a fit of pique. Instead, after some consideration, he cast some detection charms.
Harry knew that anyone who was moderately powerful and moderately knowledgeable would figure out the detection charms and a way to dismantle them. What they likely wouldn't be able to detect was the much more subtle detection ward he built into the charms. It was something Hermione had come up with. A charm on a charm. The ward wouldn't tell him if someone entered, but would tell him if someone dismantled the detection wards.
He also decided to take another tack and go check out the Riddle Mansion.
Once again he tempered his approach with caution. He had his senses stretched out to the fullest, looking for any trace of magic. He entered the house and explored it room by room. The results here were different. There were traces of much more recent magic throughout the house. As recent as a few days to a few weeks Harry was certain.