Oven appears to start, takes forever to preheat,

This is what I would do: I would unplug the range and connect my test cord to your range cord. I use an ammeter along with my test cord to read the amp draw of the bake ignitor. If it cannot get above 3.5 amps I know the ignitor is bad or weak. Since the oven is working that means there is a good circuit. In order for the safety bi-metal to open the amp draw must reach 3.5 amps or better. So to me I am thinking bad ignitor. To get to it I remove the door oven racks and bottom, I then remove the flame spreader and unplug the quick connect to the ignitor. I remove the burner and ignitor and replace the ignitor on a work bench. I am too old to be bending over and trying to do any parts replacement inside an oven. LOL. I have a training film which shows how the silicone carbide ignitor works HERE. Post a model number and I may have a service manual, do not forget to rate the answer.

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Hey- Gas ovens have burner and broil ignitors that may still function enough to ignite, but not enough to allow gas valve to fully open. Flames appear but do not have full flow of gas to reach full temp rise. Some broil/burner ignitors are the same and interchangeable, but are carbon ceramic elements and are very brittle- easily breakable! Most likely culprit is faulty oven burner ignitor available for 50-100$ at local app parts. Hope this helps- Thanks- ED