You have high incomes, so consider working out a payment deal with the contractor. Most folks are willing to work with you if you can pay them at least half when the job is completed (cover their costs). In your spot, I might pitch them the idea of 10% down, 40% when the job is completed, and 10% (4k) a month for the next five months. Or, you could exhaust the EF and repay it over a period of time from your incomes, drawing on the taxable accounts if something comes up in the meantime.
If that doesn't fly, you can use a HELOC or LOC to pay it, just be sure you understand the origination costs. Some banks throw in junk fees at various steps in the process (like an annual subscription fee). It could be cheaper to liquidate some of your taxable holdings, especially if you can get some tax harvest-able losses as part of the sale.