Congratulations, that's a great image.
I'd just like to comment on the general impression given by your question, which is fairly widespread. People often talk about jpgs looking better than the initial processed raw image. The inference is that the jpg is somehow better, (but I'm not suggesting that is your opinion). However whereas a jpg is ready for printing, (although you can somewhat alter them if you wish), a raw image MUST be processed in order for it to be usable. I suggest the aim is not to make a raw image look like a jpg, but the other way round, i.e. a jpg should should ideally match a correctly processed raw. That is not possible for many reasons, among which are due to the restricted colour space, contrast etc of the jpg embedded in the raw data.
I realise this was not the point of your original question,
the JPG preview which shows before the RAW renders looks pretty awesome and I'd like to use that.
but a correctly processed image based on raw data, has to be better than a jpg, whether it's in LR or PS. Furthermore, haven't you achieved something more pleasing to you than trying to copy the jpg!
By the way, I'm still struggling to master the techniques required!
Again, congratulations on a great shot.