FW is right. Unfortunately a common issue with the TL kits. Expanding the pickup cavity is generally the primary fix.
I am a bit dubious about enlarging the cavity with a chisel though, but that just me.

The gap in the neck won’t make up that difference, although, I’m tempted to just rasp out the corners just a little.
Just to be clear, we're talking about removing material from the corners of the heel of the neck not the pocket here. When you say "rasp out", I interpret that as from the pocket.
Whilst it may not make make up all the difference, it will make a difference overall. The better the fit, the better the end result.

Back to the bridge...

I presume the long line perpendicular to the neck is your 648mm mark. If that's the case, with your Gotoh bridge placement, routing the pickup cavity enough so the treble E saddle falls on that line and you'll be right.
However, it's best to first adjust that saddle so there's about 2mm of intonation screw thread entering the string slot of the saddle. This will allow adequate forward adjustment if needed. I have had some six saddle bridges intonate as short as 647mm. Better safe than sorry.

As for the gap between the bridge plate and pickguard, this is also very common, even on genuine Fender Tele's. A lot of little things like that go unnoticed until we start building our own guitars and putting every little detail under our personal microscopes.