Residing in USA as J-1 student, want B-2 or similar for extended travel

Be careful: your grace period does not begin with the expiration of your visa, but with the end of your program (assuming you were admitted "D/S," duration of status, as is usual with J-1 visa holders). This date should be shown on your DS-2019. If your program ended more than 30 days ago, you have already exceeded your grace period and begun accumulating unlawful presence. By contrast, if your program extends until September 30th, your grace period ends on October 30th (I assume that the grace period doesn't start until the day after your program ends, but I'm not certain of that).

I have found some websites that say you can turn your J-1 into a B-2 without leaving the USA, but I can't really find where I do that (I assume just applying for a B-2 would require me to go to the US consulate in my home country).

You can get a B-2 visa anywhere, really, except in the US. To change status while remaining in the US, you can apply to change your nonimmigrant status by filing form I-539. The fee is $370. My understanding is that you must apply before the end of your grace period.

I have found it is unwise to leave (to Canada) during the grace period and try to re-enter using VWP as it is a requirement to go to your home country (Netherlands) in between, is this correct?

There is no requirement for you to go to the Netherlands before you can use the VWP, but it may indeed be risky and unwise to try using the VWP. It is quite possible that you would be denied entry by a skeptical immigration officer, since you're unlikely to have, for example, a stable job in another country right now. If that happened, you would be in a bad situation. By contrast, if you apply for a change of status, you can stay in the US while the application is being considered, even if it is eventually refused.