You hit the nail on the head. My conclusion is to hold the "overpriced" assets that produce a solid, consistent income. I am taking the Warren Buffett view that day to day (or year to year) price fluctuations are interesting, but insufficient to divert my attention from the current income and the growth in both income and value over a long time. Trading around in real estate costs you more in transaction costs than you can make up in short term improvements in cap rate.
Right now "cash is trash" because the world is awash in liquidity. There is just too much money chasing too few assets. In my view, the liquidity will drain out of the asset markets quickly at some point and cash will become a lot more "valuable" and useful. Being an older and therefore more patient investor, I'm willing to hold on to some of that green stuff, even if I lose to inflation in the short term.
And if you have just too much green stuff, paying off a high rate mortgage is one of the better uses of cash.