Your last post outlines a reasonable plan.
I do think you should be sure to listen to your wife's ideas about just owning it outright, especially if you can find something at the lower end of your $800K-$1.5MM range. Yes, it financially might make more sense to keep the mortgage. But this is not completely financial, it is also psychological. Remember, you are in a partnership. With 6 months to a year to look, you might find the perfect place at the lower end of the range. I can't blame your wife for her outlook, because there's no way I'd ever sign on the dotted line for a $1MM mortgage, even with your assets. Don't pressure her into buying too much house or taking out a large mortgage if she is more nervous about it than you are. On the plus side, if you side with her idea, instead of having to make a mortgage payment every month, you'll have all that extra money to stash in the market, right? When the market nosedives, which it will eventually, you'll have cash flow to buy stocks while they are on sale. That will certainly feel good, and it will free up cash flow for when the kids get to high school and you start having bigger fixed expenses (like bigger grocery bills and car insurance for teenagers, ouch!)
Her peace of mind of knowing there is no mortgage payment is worth more than investment growth...Happy wife, happy life!
Edited to say I just saw your post to say you overwhelmingly have Apple stock. In that case, I am 100% on the side of your wife that you should sell some of that to pay for the home outright in cash. Just get a $1.5MM property, and thank Apple for your good fortune. I mean, you basically already hit the equivalent of the single stock lottery already. Why tempt fate by refusing to cash out some in exchange for a secure family home?