I thought LSA Art. 15 only applies to non-fixed term contracts (and contracts of more than three years). Otherwise, if the contract says nothing about your right to quit, Civil Code Art. 488 and 489 should prevail:
[quote]If the duration of hire of services is fixed, the contract of hire of services terminates with the end of that duration.
If the duration of hire of services is not fixed or can not be fixed in accordance with the nature or purpose of services, either party may terminate the contract at any time, however, if customs is in favor of the employee, such customs shall be followed.
Even though the duration of the hire of services has been agreed upon, either party may, in the event of any serious occurrence, terminate the contract before the end of such duration.
If the occurrence as specified in the preceding paragraph be due to the negligence of one of the parties, the other party may demand for the injury from him.[/quote]
If for whatever reason your resignation isn’t valid (I mean if you didn’t have the right to quit with X days’ advance notice), send another resignation notice, this time invoking Art. 14 of the Labor Standards Act. All you need is one violation of the LSA, the Enforcement Rules of the LSA, the Regulations of Leave-Taking of Workers, the Act of Gender Equality in Employment, the Labor Insurance Act, or Art. 482 to 489 of the Civil Code (not to mention a few other things), plus the fact that you became aware of the violation within the past 30 days (unpaid wages including overtime etc. are not subject to the 30 day limit). Considering how lousy employers generally are, you probably have a wide range of violations to choose from. Did you get paid for the holidays? Even the holidays that still existed last year but were widely ignored e.g. Dec. 25? etc.
If you do it this way there’s no notice period, and in addition to whatever money you’re already owed (holiday pay, overtime pay, etc.), you can also receive severance pay. Your boss hates you anyway, so why not? 
In theory, you’re supposed to file your tax return early if you leave Taiwan, but if you “intend” to return later the same year, there’s no problem.