I can think of a few things to consider and offer a few thoughts, without of course, giving true advice. You might want to run some time-value-of-money calculations on that $50,000 to see what the impact of not having that invested would be. There are a number of calculators online that you could use if, like most folks, you don't happen to have a financial calculator in your desk drawer.
Also, do you expect your tax bracket to stay the same over time? I assume from your question that you've already determined that converting the full $200K won't subject any of that income to the 32% bracket. (Also, don't forget the Net Investment Income Tax as well!)
If you expect your tax bracket to decrease in retirement, having the full tax-free option won't be quite as attractive as avoiding additional tax now. Although, none of us have a crystal ball to know how tax law changes might come into play there, too, but assuming tax brackets stay steady, would you remain in the 24% bracket in retirement as well? Of course, the Roth IRA also offers some other benefits such as not being subject to required minimum distributions (RMDs), though you're still a good time away from that concern.
My first thought would be to make the changes over time so that you could do it in small pieces. You could pay the tax out of your current salary or savings, instead of using your retirement funds to pay the tax. This allows more of your money to stay invested - whether in the tax-free Roth or the tax-deferred 403b. More money working for you is usually a good thing, but you do have some time on your side as well - but how much time, of course, depends on the mix of your investments and how aggressive those may be along with when you expect to need the funds.
Not knowing your overall risk tolerance, but assuming that you'd be somewhat tempered due to the proximity to retirement age, I wouldn't plan with more than a 5%-6% expected return when trying to determine the best course of action.
It is also worth considering some of the other differences between the types of accounts including different tax rules for early withdrawals (a very minor point in your case due to your current age) and the fact that you may have lower costs in your 403b account than in an individual account (sometimes significantly so). The cost of your underlying investments can, over time, have a real drag on investment performance. Of course, I don't have enough information to compare those for you but the information is typically readily available from the firm that manages your 403b. You often trade those lower costs, though, for less choice in underlying investments - yet another factor to consider.
You may also wish to compare the costs and investment selection of your current 403b provider with your former, as well, to see if you would benefit from transferring assets into that account, if the plan allows for that.
Overall, though, my gut feeling is generally to convert each year only what you can afford to pay taxes on without using the retirement funds to do so. This allows more of your money to work for you over time.
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