As you note, your question is inherently opinion-based. That said, if I were in your situation I would sell the stock all at once and buy whatever it is you want to buy (hopefully some index ETF or mutual fund).
According to what I see, the current value of the HD stock is about $8500 and the JNJ stock is worth less than $500. With a total investment of less than $10,000, any gain you are likely to miss by liquidating now is not going to be huge in absolute terms.
This is doubly true since you were given the stock, so you have no specific reason to believe it will do well at all. If you had picked it yourself based on careful analysis, it could be worth keeping if you "believed in yourself" (or even if you just wanted to test your acumen), but as it is the stock is essentially random. Even if you want to pursue an aggressive allocation, it doesn't make sense to allocate everything to one stock for no reason. If you were going to put everything in one stock, you'd want it to be a stock you had analyzed and picked. (I still think it would be a bad idea, but at least it would be a more defensible idea.)
So I would say the risk of your lopsided allocation (just two companies, with more than 90% of the value in just one) outweighs any risk of missing out on a gain. If news breaks tomorrow that the CEO of Home Depot has been embezzling (or if Trump decides to go on the Twitter warpath for some reason), your investment could disappear.
Another common way to think about it is: if you had $9000 today to buy stocks with, would you buy $8500 worth of HD and $500 worth of JNJ? If not, it probably doesn't make sense to hold them just because you happen to have them.
The only potential exception to my advice above would be tax considerations. You didn't mention what your basis in the stock is. Looking at historical prices, it looks like if all the stock was 20 years old you'd have a gain of about $8000, and if all of it was 10 years old you'd have a gain of about $6000. If your tax situation is such that selling all the stock at once would push you into a higher tax bracket, it might make sense to sell only enough to fit into your current bracket, and sell the rest next year. However, I think this situation is unlikely because: A) since the stock has been held for a long time, most of the gains will be at the lower long-term rate; B) if you have solid income, you can probably afford the tax; and C) if you don't have solid income, your long-term capital gains rate will likely be zero.