Recharacterizations are based on dollar value and the overall change in dollar value of the IRA, not in the performance of any particular investment within the IRA. The recharacterization can be accomplished either in cash or by an in-kind transfer of any shares having the required dollar value.
Capital cost basis has no meaning within an IRA. Ignoring any brokerage transaction fees that might apply, there is essentially no difference between doing an in-kind transfer to accomplish the recharacterization from a traditional IRA to a Roth IRA and selling the shares within the traditional IRA, transferring the cash to the Roth IRA and repurchasing the shares in the Roth IRA. The only difference with doing it in cash is that the sales price will likely be a bit different from the repurchase price. Either way, a recharacterization is a nontaxable transfer of a particular dollar value.
If you choose to do an in-kind transfer, it would make sense to choose shares that have the best chance for future appreciation since that appreciation will be tax free (once your Roth IRAs are qualified) in the Roth IRA instead of tax deferred in the traditional IRA. Past performance is not a factor.
