In my accent, lover, hover and clover have three different vowels in the first syllable. Plover rhymes with lover for me. Does it rhyme with clover for you?

Yeah, it does.

I suspect it's not the standard pronunciation in my region, since Wiktionary lists it as an alternative American pronunciation and I'm Australian, but for whatever reason that's how I pronounce it.

I expect that many people pronounce "plover" as "clover" if they saw it written down first before they heard someone who knows the pronunciation say it. There are plenty of words like that in English.

I pronounced it as rhyming with "clover" too before learning that it's actually incorrect.

That's possible too, though I don't subscribe to the idea that a widely used pronunciation can be incorrect.

And mover has a fourth, now that I think about it.

I think GP was alluding to the drug P (meth).

A simpler explanation would be "pee-lover".