@Account Closed, I don't know why Bob goes on these tirades, but he's easily ignored. The other 99.99% of people on here are more helpful, or at the very least they're more polite.
You were very clear and your idea makes sense. I would double check with a 1031 expert/CPA to ensure you correctly understand all the tax ramifications of a 1031, but it's my understanding that if you trade-up everything is deferred, and you begin depreciating the difference in the larger property. If your grandmother is no longer able to depreciate the property she currently owns that removes one of the advantages of a rental, which could be helpful in shielding some of her other income from taxes.
How you invest her $400k depends a lot on what she wants, but if she's looking for cashflow it would seem that small apartments in a more affordable corner of the country that aren't over-leveraged would be the right call. I have a similar situation with my mother, who is looking to 1031 some properties to put into a small apartment building to make everything easier on her, but I think it's time for a property manager to take over. I saw some mentions of the continued property appreciation, but I feel that someone towards the end of life isn't concerned with that unless they are more concerned with their heirs than their living expenses. Certainly, you will have to take into account rent appreciation and the difference in property taxes to get a good assessment, but finding the right deal should prove easy as long as you're not in a hurry.
Good luck!