Hi Ben, the tuners don't look too bad, call it 2.1mm out with the measurements you took between holes. The main thing for me is that they are aligned is more obvious to the eye than distance between tuners. So are the pickguard holes pre-drilled and some don't align ? If this is the case drill new holes and the pre-drilled holes will be covered by the pickguard (hopefully !). Otherwise wood glue and sawdust of a similar colour or glue toothpicks or thin dowel in the holes as Doc explained.
The gap between pickguard and overhanging fingerboard is normal.
Check the distance nut to 12th fret and 12th fret to bridge saddles, they should be roughly the same (12th fret to low E saddle about 3mm more). Most tele kits I've built the bridge pup cavity is a bit far too south and I've had to route the neck side of the cavity by about 5mm and this will close up the gap between the bridge plate and pickguard. If you order from Realtone today by express post they should arrive xmas eve Thursday.
Upgrades sound great, so I'd order your Wilkinson bridge as soon as you can so you can check intonation and make sure bridge pup sits in the cavity nicely.
The Tonerider pups are great value for money I recommend them.
I thought the TL-1AR was alder body but it's ash, so think the model is TLA-1 with rosewood fingerboard. Some nice looking grain