I've just resigned my current position, giving two weeks notice (but not really). I'll be on vacation until the last day of my resignation (had to start the new position before the end of the year and had already planned a vacation).

I was given the following options:

Have my resignation effective on the day of my resignation letter.
Work the next week, then be paid for the remainder of my vacation.

Do I have any options my employer is not disclosing? Ideally, I'd like to be able to use the remainder of my vacation (4 days), then take the next week of paid company holiday, and return to work for 1 day next year.

Here is the company policy:

If, however, after due consideration the employee decides to leave, it
is requested that the employee provide the Company with a written two-week advance noticeperiod (vacation days or paid time off days may not be included in the two-week notice period).
The Company will only compensate employees for unused pro-rated vacation when the employee works throughout the notice period, and is not terminated for gross misconduct or cause; otherwise, unused vacation will be forfeited. If, as sometimes happens, the employee's supervisor wishes for the employee to leave prior to the end of the employee's two-weeks notice,
the employee may be paid for the remainder of that period.

Your employer didn't have to give you any options at all. They could have accepted your resignation immediately and shown you the door. I'm sure what you describe as your ideal situation would work nicely for you, but they have absolutely no legal obligation to let you do it. Why should they?

Accept one of the options they gave you and be glad they gave you a choice.