I'll probably buy a house in the next 3ish years.
Why would you wait three years to buy a house? Not sure if you are staying in the area? Houses too expensive? Enjoy renting? These are things to consider.
In your shoes (which I'm not): If I liked the area and intended to stay I would probably start looking for a house now. Rates are still low and with the potential of having a large down payment you might get very good rates. I would also view a house as not only someplace for me to live but as a potential rental should I move on. Depending on the cost of houses in your area, and other factors asked, I might consider cashing in enough of the stocks to buy a house outright. I'd need a lot more information to make that determination.
I didn't look up your stocks. What is their long term (10 years or more) history? Is the price stable, do they have a long history of paying dividends? Are they likely to be seriously impacted but the current oil roller coaster?
In my opinion the worst thing you can do now is to be in a hurry to do something. Unless you have reason to believe the value of your stocks will crash and not recover, take a break. Explore your options. Give yourself time to think.
Good luck.