Looking for a drama where despite the ML’s riches, good looks and charisma, she isn’t moved at all by him and will fall for the SML or other guys, making the chase interesting and yet he’s relentlessly pursuing her showing himself off with his money or sexiness. Thanks! The only one so far that fits the bill is “what’s wrong with Secretary Kim?”.

I think Secret Garden and Falling For Innocence fit your description. I hope you will like it.

https://mydramalist.com/2687-the-bean-chaff-of-my-life

••https://www13.watchasian.co/drama-detail/bean-chaff-of-my-life

ML has good looks and charisma, riches not so much. But that's really not important here.

Also, it takes place over 12 years and you pick up a bit of a history lesson about Korea during those years.   

Each of the 16 episodes has one musical number, sometimes a song, sometimes a song & dance. Here's the finale from YouTube. 

https://www.youtube.com/watch?v=ps4CXBZ0KIA (4:47)

Take a chance on Bean Chaff.

Ok in some of them I am not sure which one is the ML, but here you go 

I second the Secret Garden, also

The Greatest Love  

Noble, My love

Protect the Boss

The ones above are similar to What's Wrong with Secretary Kim. 

The ones below can be quite heavy and dramatic, they are not romcoms , but have an unwilling female lead that is chased by a guy.

When a Man is in Love 

Empress Ki

Love in Sadness 

currently airing:   Before we get married     Bit of a twist though, FL  has a boring/regimented fiance and bumps into the ML.  He falls for her and pursues her relentlessly while she tries to rationalize and stick to her plan with her fiance.   ML is much better catch and sexy, but gets tons of rejection from her and the pursuit is in full gear.  

Love better than immortality