A lot of the problem appears to be due to the supplied 6-saddle bridge. The saddles just seem to me to be way too far away from the bridge pickup. On my Fender Korean Tele, the top E saddle is about 20mm away from the corresponding edge of the pickup. You're about 5mm away from achieving that at 25mm even with the saddle as far forward as it will go with only a bit of thread left in the hole.
Is this a through strung bridge or a rear-loading one? If through strung with pre-drilled holes, you're rather stuck as to bridge position, regardless of the pickup rout position.
One solution would be to find some longer threaded machine screws of the right size. I'm afraid I have no idea what they'll be, but hopefully they will be a standard metric thread, probably either M2, M2.5 or M3. But you may then also need longer tensioning springs.
I was contemplating just buying a different bridge with saddles that are much closer to the pickup. I don't have the tools to modify the body and pickguard. Just unfortunate that I have to spend additional money to replace parts just to get it to work. Luckily no bridge holes are pre-drilled so installing a different bridge won't be an issue.