but my understanding is to do this I cannot have any pre-existing tIRA accounts. Am I correct here?
Not exactly. You can look up the pro rata rule for backdoor Roths, but basically the pre-tax and post-tax money that gets converted is in proportion to what is in your IRAs. For example if you have 6,000 of pretax traditional ira, and 4,000 of post-tax ira, whatever you convert will incur taxes on 6/10ths of the amount.
You would have to look at your overall situation to say if this is a good idea.
You should also note that if your work 401K is pretty good, most plans will allow you to roll over your pretax traditional IRA into your 401K with no tax consequences.