The best replacement for twill is poplin.

The best alternatives to twill are rated as following:
★★★★★  poplin
★★★★  canvas
★★★★  chino
★★★  ripstop
★★  denim
★★  oxford
★★  pinpoint
★  herringbone
★  linen
★  broadcloth
★  poplin shirt
★  tweed
★  microfiber
★  plain weave
  gabardine
  sailcloth
  diamond weave
  duck
  brushed canvas
  sateen
  flannel
  duck fabric
  birdseye
  khaki
  microsuede
  percale

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Google Trends

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twill
poplin
canvas