"Dense upright growth" is not the typical growth habit for oakleaf hydrangeas. They do tend to be rather rangy but if well-sited and healthy, the foliage should be dense enough during the growing season that this ranginess is not obvious. Here is an image of a mature Amethyst from a Polish website - very sprawly and not at all upright:
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You can prune if you like.....not sure that would produce results that are what you are looking for. And be aware that pruning now will both eliminate flowering potential for next season as well as likely producing new late season growth that could more easily be damaged by winter cold.

you are a newb.. right ..

i think the only failure here.. is your expectation of what you want it to look like.. vs what it is .. and how littel time you have given it ... presuming it wasnt a 10 foot transplant ....

ignore it for 3 years.. focusing on other things..

and in 3 years.. you will be amazed ...

dont over analyze it all.. give your garden time to develop ...

if you want any real opinions.. you will have to post a pic ...

ken

Sorry, I just saw these responses... thought I had signed up for email alerts.

Ken, yes, I am a newbie. I moved into an old house with virtually zero landscaping (aside from the inevitable azaleas and nandinas etc. - that older hydrangea was actually a 10' transplant I got from a neighbor) a few years ago, and have been transforming the yard into a garden during the past three years.

I'm fine giving the shrub time. I have just been stunned by how huge it has gotten in the three years since I planted it, and was wondering if I should cut it back a bit and thereby could encourage denser growth. I thought pruning through July was fine with regard to next year's flowering. But it sounds like I might better leave it alone.

Thanks for the advice!