If you have time series then HL must have a lot of info on covariance, and shouldn't be ignored. You don't know exactly the intraday time of HL, but you know the day. There must be MLE of covariance that takes into account HL and OC

Are there other greeks for this option? The reason I'm asking is because when the greeks are missing in the feed for us it's usually when the option can't be priced given the inputs, i.e. thinly traded options where the prices are either stale prices or quotes.

@vdesai, added Kalman filter suggestion

R's help is pretty much useless unless you know how the function works already

where did you get this equation from? specifically, the right hand side of it. please, refer to some text so we can see where you're wrong