Is it sufficient, in order to close the door to minor shirk, that I ask Allah to facilitate my need with good expectations and reliance on Him, and then take the necessary means?

The believer is commanded to utilize means and rely upon Allah, while believing that results are only achieved by His permission. What the questioner is doing — supplicating Allah and asking Him to facilitate her needs with goodly presumption and reliance upon Him, then utilizing means — is what is religiously required. She must not open the door to obsessive doubts and suspicions, especially concerning matters of creed.