Thanks for the feedback, guys.
To clarify: we will not qualify for any sort of mortgage, so I have no particular concerns about what lenders think of our savings/investments/etc.
Keeping cash on hand is likewise useless, since we are basically locked into paying cash for a new house (and selling our current one to do it, since we're talking about million dollar houses here). There will be no "downpayment" involved, as we can't finance any meaningful portion of the purchase.
I'm looking at this as a guaranteed 3.75% return, as an alternative to just sticking money in a savings account or CD. Now, if we were planning to stay in the house long term, that would be pretty crappy, since we could do better in the market. But given the situation (house HAS to be sold to move, move will probably happen relatively soon) the potential volatility of the market is unappealing.
BTW, the AirBnB was too much hassle, so our apartment is now rented long term. It's a nice easy way to net $15k a year, which will be a bummer to give up if we do end up moving. C'est la vie.
-W