grammar - "Would you mind if I write X?" vs. "Would you mind if I wrote X?"

To my ears it sounds like "Would you mind if I wrote..?" is more of an "in theory" question, while "Do you mind if I write ..?" is the way you would phrase when standing right next to a sign-up list with your mate and presenting him with an actual choice. Also I don't think it's correct to use "would" + present tense.

Should he confirm the latter question, you're GOING to write his name on the list. Asking "Would you mind if I wrote.." feels like asking someone if he'd generally object or agree to you writing his name on that list.

Anyway: Out of those two choices you gave, the correct one is "Would you mind if I wrote".