My 2 Cents, in response to your questions above:
*The stock market is going down at this moment. Is this a good time to buy new Vanguard shares with money that is making no interest in a money market savings account? Don't try to Time the Market. If you have cash (that you won't need in the next 5 years or so), just invest and move on with your life. Remember that the reason so many people invest is that the market "always" goes up in 20-30 year timelines. That's the timeline that is relevant to eventual retirees.
*How should we divide up our savings between adding to Vanguard taxable funds, Vanguard Roths, paying off mortgage, and our individual TSPs? We love the idea of paying off the mortgage quickly but are thinking it makes more sense to let our savings build and then paying it off in a lump sum rather than over time, but the math makes our brains hurt. Should we occasionally pay an extra amount toward the principal? How often?
0. Agree with E-Fund. Your jobs are very stable with the Government, maybe increase to at least 1 month E-Fund in case there is a work stoppage or something like that (to 7.5 K or so). This depends on your risk tolerance too.
1. Max out your TSP's first (18500 each in 2018, 19000 beginning 2019). There are huge tax benefits to this, and you get your employer match as well. Then adjust your fed withholding so you don't get a huge tax refund. You want to break even with tax withholding and improve your month to month cash-flow.
2. With your joint incomes and tax brackets, I would focus on Roth IRA's next. 5500 each in 2018, 6000 each in 2019
3. After that, add to Taxable until you have enough to pay off your mortgage in one go. Remember that your cash flow will impacted negatively if you add extra payments to your mortgage, but won't be impacted if you continue to build your "pay off the mortgage" Taxable account. Once you get to that number, you can decide if you really want to pay it off or not. Fireby35 is right about the math.
*How should we set up a Roth IRA conversion ladder from our assets? Is this better managed through just one of us rather than two? How soon should we set this up? Is it better to use a Vanguard Roth or a TSP Roth? Is it possible to do tax-free Roth conversions when one partner is still working -- even part time / hourly?
Lots of questions here. Like I said above, the math and federal tax benefits favor maximizing the TSP's Pre-tax. The Roth Conversion ladder is only worth doing once your joint incomes is much lower, because you have to pay the extra tax on the conversions from your taxable (i.e. you want to do this when your top tax rate is 12%, not 22%). JOINT INCOME is most important, regardless of how you get there with partner A or partner B's incomes.
*Should I consider doing a withdrawal from TSP to do a rollover into an IRA (this has to be traditional, right?) so that I can begin doing annual Roth conversions in the zero tax bracket and take the money out tax-free starting 5 years later? Does it matter whether the TSP money to be moved is marked traditional or Roth? ----> NO, probably not the best idea at your income levels right now
*Any other obvious ways we could be smarter about savings, taxes and the accounts we have set up? See above
*Any other info I can provide?
If you haven't done so already, create an Investor Policy Statement, and stick to your IPS long term. Bogelheads.org is a great site for additional investing education.
Let me know if any of the above doesn't make any sense. It can get complicated.
All the best, JGS
P.S. Always listen to MDM, he knows what he is talking about.