1) Double sided tape. Easiest. 

Downsides: Concerns about how secure it will be in the long term. 

2) Plastic push pins superglued to underside of pickguard and pushed into existing screwholes. 

Downside: Additional concerns about how secure they'll be. Will have to route a hole the size of the push pin head so pickguard doesn't float above body. *Probably a bad idea.*

3) Superglue nylon bushings (like one in the picture) underneath the pickguard, route holes through the body to fit bushings. Route holes on backside of guitar to place securing screws through. This will be the most secure method. Removing the pickguard will be just as simple as a normal strat pickguard. IMO will be the cleanest solution despite having to drill holes in the back.

Downside: Requires the most work. Little room for error. There will be 8 or 9 holes in the back of my guitar but the front will look clean as hell; I will never be able to sell it (not like I'll ever want to).

  
If anyone else has additional ideas for mounting a pickguard with no screws I would like to hear it. Or if anyone has improvements for these ideas I would like to hear them.

This is a really stupid idea but I'm hooked on the look so I'm gonna do it anyways. It all just comes down to how I achieve this.

No Screws on pickguard for clean look