Planning to run away for the summer and need tips

Hi, I plan to run away in the summer of 2026 with my friend. I am 15 and he is 17. Our home lives are kind of sort of fine other than issues with my parents but I have a roof over my head and a stable life, which I am so grateful for. We are going to come back before the school year starts, i know it sounds dumb but I just want to get away from my controlling mother and be independent for a little bit. We've fleshed out an outline of a plan and have months to prepare but I would like tips from real people because I want to prioritize safety.

My plan is to say I'm sleeping over at my friend's house, those sleepovers are the only time my mom isn't monitoring my every move. That gives me until the morning after to hopefully cross state lines. I don't plan on telling that friend anything but I'll drop my phone in her backyard and put it in a couple  ziplock bags. I'll schedule a text to my mom for noon the day after saying something along the lines of "im leaving i'll come back before the school year starts i'm safe and have a plan i'm so sorry for making you worry" and leave a note saying the same thing in the ziplock bag for good measure. My mom tracks my location so they'll find the phone within the day after or so. Hopefully I'll have a burner phone I can use at this point.

Basically after taking care of the phone we'll meet up and go to some bathroom so i can cut and dye my hair- i dont know if this will make much of. a difference but i might as well try to change my appearance. Now the thing is transportation. I feel like it's pretty stupid to take something like Amtrak because i'm pretty sure you need a valid id for that and we are not about to have our names on file anywhere. I live on the east coast and we want to go straight south to New Orleans and then work our way back up north on the east coast hitting savanah, atlanta, etc, avoiding our home state. Hopefully we can go to some big cities all the way up north and then come back home a little more than a month later. We want to spend only a few days in each city, saving time. Now this is a lot of travel and we only have so much money to get around by bus. Are greyhound buses good for this? Do we need to provide any kind of ID for buses? Is there any better ways to get to our destinations. I know this whole plan sounds so incredibly stupid but i feel like it'll be worth all the consequences assuming we'll stay safe.

Here are my questions:

-Most efficient travel, and is our plan even doable?

-Phones: My friend wants to keep his phone on him, and his parents are so much chiller than mine and honestly wouldnt mind if he disappears but im still worried about that phone getting tracked. He wants to keep his stupid 1000 day duolingo streak up. Any advice on this? is it possible for him to bring his phone and if it is what do we have to do to make it not trackable. I'm planning on buying a burner phone so like how do i do that.

-Shelter- Is there any way we can find some cheap motels every now and then that would let us book a room? Like we'll still be minors but is there any way. Is bringing a small tent a good idea- we'll most likely end up on the streets most nights so safety tips for that

-Staying clean: I'm thinking that grocery store bathrooms, dry shampoo, maybe paying ten dollars for a gym membership so we can use the showers  and then cancel the same day or something?

-Police: My mom will 100% be looking for me, so if i clarify that i am safe etc will the police still be looking for me? What about the ai recognition technology thing with public security cameras. Do we have to worry about that? Basically how far will the police go in this situation.

-Just literally anything- Please call me out if any part of this plan is super stupid, which im sure a lot of it is. Anything that will get us caught, any tips you have will be so appreciated.