If it is exactly as stated - $35K qualified dividends, no other income of any kind, then you can convert up to your standard deduction + exemptions with no federal income tax.
So, with your numbers, ignoring things like ACA subsidies, you should convert $28,800, then tax-gain harvest 11,500 if you can to step up your basis. That gives you 28,800 - ordinary income at 0%, 35,000 qualified dividends at 0%, 11,500 long term capital gains at 0% = $75300 - the top of the 0% qualified dividend / long term capital gains bracket for MFJ (2016).
Edited to fix numbers - was looking at the wrong chart.