So you can rollover to the 403B at any time - that means there isn't much risk to either approach so pick one and do it. It sounds like you don't need to do the Backdoor Roth at this time.
So, there are multiple uses for Roth conversions, but the basic purpose is "pay tax now, and change the amount converted from traditional to Roth". During the accumulation phase, if your income is too high for regular Roth contributions, you can use a backdoor Roth IRA to get money in to a tax advantaged account you otherwise couldn't. If your 403B has the requisite features, you might even do a "Megabackdoor Roth" at some point. As you get to early retirement, you might do a Roth-IRA ladder to get your money out of your traditional accounts gradually. Even after you're 59.5 and don't have to do conversions to finagle penalty-free withdrawals, you might do a conversion because you like the tax rate you'll pay today vs. your likely tax rate later.
The only use of the Roth conversion that having other tIRA money out there screws up is the backdoor Roth IRA, as far as I know. That is because, when you do a backdoor Roth IRA, you are converting non-deductible tIRA contributions. But when you do this, remember that 1) you aggregate all of your tIRA accounts and then 2) pro-rate the non-deductible and deductible tIRA portions. So if you put $5K in to your tIRA in an attempt to do a backdoor Roth, then convert $5K, but you have $95K in tIRA money out there from an old rollover, you'll pay tax on 95% of that conversion - not what you were trying to do.
Occurs to me we might be talking about two different things, so list of terms as I mean them.
Backdoor Roth - a technique to get around Income limits for Roth IRA contributions. Make a non-deductible contribution to tIRA, then more or less immediately convert to Roth. You can get $5500 into your Roth IRA this way when you otherwise could not.
MegaBackdoor Roth - if your 401K or 403B allows, a way to get a lot of money into your Roth IRA. Make after-tax contributions (not Roth) to 401K/403B, then rollover/convert to Roth IRA. You can cover the gap between your traditional or Roth election + any employer contributions up to the $54K limit, so you can potentially put a lot of money into a Roth IRA via this channel. No concerns about pro-ration on this, per IRS guidance.
http://www.madfientist.com/after-tax-contributions/Roth Conversion Ladder - convert money today, paying any tax owed, so you can withdraw the conversion amount tax and penalty free after the conversion is aged for 5 years. Repeat conversion in 1 year for money to be withdrawn in 6 years and so on. Usually used to bridge from FIRE date to age 59.5.
