How they should have moved Harry in deathly hallows if Rowling didn’t want us to witness an epic chase!

1) Brooms/thestral/motorcycle and then apparate as soon as the fight starts.

There will be so many spells near Harry once the fighting starts that the whole ‘around Harry we can only use magic the ministry can’t detect’ goes completely out the window. The ministry also can’t report the incident because they are trying to hush up attacks like that and they don’t want people to know there has been another mass Azkaban breakout. BTW we know that’s true because that’s what happens in the book!

We also know you can apparate on a broom because Mundungus does it when he spots Voldemort.

This seems the logical and safest thing to do. Harry can apparate by this point and even if he’s not passed the test, someone could side apparate him.

2) A closer safe house

Set up a safe house with all the spells they put on the burrow and Tonk’s parents house etc except choose one just outside the protective bubble if Harry’s mothers charm. So far enough that their magic isn’t detected by Harry’s trace but near enough that there is literally only seconds where Harry is exposed walking from one to the other. Then have a portkey in that house much like they did at Tonk’s. The order could buy/borrow/rent a property for this purpose.

(A slight precaution…you may need to trick Harry into thinking he is going back to the Dursleys for just one night after that. That way he still thinks of the Dursleys as his official home and doesn’t risk the charm failing as soon as he leaves thinking he’ll never return. Not 100% sure this is necessary but still.)

3) S-Muggle him out

Harry’s mother protective charm is deceived almost like a bubble (a bit like how Harry visualises Tonk’s parents’ house protection). Moody refers to when they exit the boundaries of the charm etc so it clearly has a reasonably definite limit spatially. This is why they drive the Dursleys a certain distance out before apparating, although obviously that’s also in part due to Harry’s trace.

Anyway, even if you disagree with some of those details, he point is that Harry is protected briefly and then at some point he is not.

So you send him polyjuice potion (by owl or muggle post or in person via Mrs Figg, whatever) to change into a random muggle. It’s in a hip flask.

You get Harry to pack his things into a rucksack. Leave the big stuff like the firebolt or Hedwig. He could hide the firebolt under the floorboard for later collection or give to Mrs Figg or abandonment to the deatheaters.

He puts in his cloak before the charm breaks, spins a bottle or something and starts walking in that random direction. He just walks out of the charm protected by the cloak. He keeps walking for about 2 hours. Once he reaches wherever that is, he looks for a muggle train station, finds a toilet cubicle, takes off the cloak and takes the potion. He then walks out onto the station platform as a muggle and uses the muggle train system to go to wherever the safe house is or to a secure/protected (like at Tonk’s house) portkey to achieve the same thing. He has the hip flask so will take polyjuice each hour to stay a random muggle.