I’m pretty sure the coax cable doesn’t act as an antenna. Loops larger than a few cm shouldn’t matter either. The only bit that will act as an antenna is the 4-5cm copper U-shaped loop at the top of the plastic pad.
As long as the top of the aerial isn’t covered by the aluminium foil at the back of the lid, you should be fine. You’ve probably seen these before/after pictures of mine already.
Only argument for shorter cables is that they might provide a stronger signal… but I’m not keen on soldering on plastic PCBs (whatever they’re called) just to find out… always a very messy job.
Hope you find your missing bits mate! I sometimes find screws embedded in my flip-flops for some reason! Oh, and… 300Mbps? I need a new router 😉