One of the strongest arguments against FEC limits on
  speech is that many (very long-term) incumbent politicians
  support it.

If I was a politician, I would attempt to capture both the benefits of big-money politics and the benefits of public opposition to big-money politics.

So, in my public speeches to voters I would claim I was 100% in favour of campaign finance reform - I'm concerned, just like you! I don't like these million-dollar donors, I got into politics to represent normal Americans like yourself! Unfortunately until the system changes I have to go along with it, obviously, so I will be taking some million-dollar donations. Once elected I'll get on that reform as soon as I can, honest! First I have to fix the economy/ensure national security/balance the budget/ban guns/fight terrorism/take on the banks/fix the college tuition bubble/deal with income inequality/reform patents/fix contraception access/educate more scientists/fix agricultural subsidies/reduce our dependence on foreign energy/reform immigration/fix the DHS/stand up to Putin/bring peace to the middle east/kiss this baby. As soon as those are done, campaign finance reform will be my top priority.

Hence, I'd get the money of the big donors without alienating regular voters by publicly supporting the current (messed up) state of campaign finance.