The best replacement for pinpoint is broadcloth.

The best alternatives to pinpoint are rated as following:
★★★★★  broadcloth
★★★  poplin
★★★  oxford
★★  spread collar
★★  twill
★  platform serve
★  percale
★  pinpoint
★  supima
  oxford cloth
  oxford shirt
  stayfast
  cutera
  pin point
  broadcloth shirts
  sailcloth

Your alternative for pinpoint is not listed? Suggest!
Speaking about pinpoint, one probably shouldn't forget about metal detector.

Other search terms related to pinpoint and their ratings are:
★★★★★ metal detector
★★★ bounty hunter
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Google Trends

Scale is based on the average worldwide traffic of pinpoint in all years. Click on graph for more.
pinpoint
broadcloth
poplin