I think you may have this backwards. If you made non-deductible contributions to your traditional IRA, then these would not be taxable, and wouldn't present a problem for a future conversion.
Do you mean that you have a large existing deductible IRA? That is usually the problem for people who want to convert to Roth, as there is no way to separate the non-deductible funds, and so the conversion will be taxed in proportion.
If that's the case, then I have heard that a strategy is to roll a deductible IRA into a 401(k) to get it out of the way. I don't think that it needs to be the same funds, just the same type of arrangement.
I'm interested how you sort this out, because I have similar problems.