What is the best way to replace a cracked screen?

I dropped my iPhone 6s on asphalt a few weeks ago and the screen cracked. Mostly at the top of the phone out of the area where the LCD is, but there are a few long cracks that run down the entire screen. I don't know if Apple Care or insurance from AT&T covers this, but I don't have it anyway. On Apple's website it says it would cost $129 to replace this screen. At a local mall there is a vendor who repairs screens so I asked him how much it would cost. He looked at it and said $150 so I decided to go to Apple. They told me that they would not repair it as there is a small crack in the top left corner of the phone itself and they are not sure whether the phone would stay together after they took the screen out. They offered to replace the phone for $299 which I don't want to do until I'm sure there is no other option. So this is where I need help: How likely is it that the phone really wouldn't stay together after replacing the screen? When I asked the vendor at the mall he didn't raise any concerns about it, but perhaps he's never seen that type of damage before. Should I trust a vendor like that? I originally wanted to replace it myself but I couldn't find an LCD screen that is cheaper than the cost of letting someone else repair it. And someone with more experience replacing screens would probably do a better job than myself anyway.

I also need to replace the taptic engine inside as the phone no longer vibrates. Would it be safe to do this after someone else has replaced the screen? (Open the phone again) Any help on what to do to safely replace my phone's screen or any thoughts on this at tall would be great! Here are some pictures of the screen and the crack in the top left side of the aluminum body: