You have some options but they each have warts. I think your best course is to talk with a real estate broker and a mortgage broker about this and see what they suggest.
IF your time horizon for the need of a bridge is less than 60 days, you can withdraw from the Roth, sell the old house and use the proceeds from the sale of the old house to make a rollover controbution back to the Roth. This is somewhat of your variation of using the Roth but with the opportunity to replace the money withdrawn with careful planning.
Take out a mortgage (or a HELOC) on the old house and use the proceeds to buy the new house, but that would only work is the old house is worth $1.25m or more so you can borrow $1.0m using the $1.25m+ home as collateral.
For this or even for buying the new house with a mortgage, you can set up periodc transfers from the Roth as "income" (odd, but true).
What my sister has done a couple times, including now, is to sell her home, move her things into storage, move into a rental temporarily and then buy the new home.
My wife and I are looking at a similar situation with a local move within two years. Our requirements, local market, and neighborhood preferences are such that selling our current house, then targeting one to buy within a couple of weeks, isn't going to work. IMHO, doing this in 2019 is how we've ended up in a neighborhood we want to leave.
We will use savings and money withdrawn from retirement accounts to cover direct costs of moving, such as real estate commission, closing costs, cost of preparing our house to sell, and hiring movers. But we don't want to use retirement savings to add to our down payment. With the possibility of renovations needed to move into an older neighborhood, we don't want to use a 60 day rollover of retirement funds to buy.
With those sources of money eliminated, there seems to be three options:
1. Take out a HELOC on our current house as a down payment to buy the new one, paying it off when the our current house sells. Is a bank going to allow a HELOC as a source of funds for a down payment?
2. Take out a bridge loan to replace the equity of our current house in buying the new one. We will have a permanent mortgage on the new house, of no more than 50% LTV. We would easily qualify for the permanent mortgage on pension and Social Security income alone.
3. Moving into an apartment while we shop for our next house. This adds the expense of two moves, plus the cost of storing tools, lawn equipment, and outdoor gear while in the apartment. The advantage of this is that we can try out whether we'd like to live in an apartment of condo long-term as we age.
Does anyone have experience or recommendations on this process?