Code J simply indicates that a distribution was paid to you from a Roth IRA before you reached age 59½. It says nothing about what you did with what was distributed. Had the asset been transferred directly to another Roth IRA by the original Roth IRA custodian, there would have been nothing to report, no Form 1099-R at all.
It's still not clear to me exactly what was distributed from the original Roth IRA. If it was cash and then that cash was used to purchase a capital investment outside of a Roth IRA, I don't think that you could justify self-certifying that you would qualify for a waiver of the 60-day rollover deadline. The only listed reason might seem to apply is that the distribution was deposited into an remained in an account that the taxpayer mistakenly thought was an eligible retirement plan, but using the cash for buying and selling something outside of a Roth IRA typically disqualifies one from getting a waiver of the rollover deadline.
If the distribution from the original Roth IRA was instead an in-kind distribution of, say, shares of a mutual fund, those shares while outside of a Roth IRA could produce dividend and capital gains distributions that would be reported on a Form 1099-DIV. In that case, the shares and the resulting distribution would have to be rolled over together to the new Roth IRA. Because the Form 1099-DIV was in your name, it would have to be reported on your tax return but then subtracted back out using the nominee process. Still, the fact that there were taxes withheld doesn't square with a distribution that was entirely an in-kind distribution. For there to have been tax withholding, the distribution had to include at least as much cash as was withheld for taxes; taxes are paid in cash.
If you received a Form 1099-B, that creates a somewhat different scenario, one that likely precludes you from rolling over the distribution from the original Roth IRA.
