Your plan is very realistic and very very common. There is a "third" type of alternative service(1. regular 2. specialist) that you can apply for which requires you to find a real job (go through interviews just like a regular job search) and once a company promises to hire you, you then apply for alternative service with them as your "sponsor". This, however, requires you to work for the same company for three years. You still have to go through basic training first in "chen gong ling" in Taichung for 3 weeks. Pros and cons to this one...but since you plan to do your alt. service via research work then this will be your only option. PhD age limit is 27, which means you can defer (postpone) your military service in pursuit of your PhD degree up until the age of 27. If you hit this limit and still have not graduated then you will have to finish military first then complete your PhD afterwards.
Getting into alternative service depends on many factors, there are 4 main requirements that I know of:
1) Family issue: such as single parent family who is at least (if I remember correctly) 65 years old or extremely poor family that needs children to support them through work.
2) Specialist: english specialist. The easiest way for you to apply through this option is to have a university (or higher) diploma from a English speaking country (doesn't matter what major you studied). If you don't, then a english teaching certificate from Taiwan.
3) 3 year work program: apply for any job you like through normal interview process. Once you get hired you then apply for alternative service with that company as your sponsor. MUST work for 3 years with the same company to fulfill your military service requirement.
4) Physical issue: mental, heart problem, lung cancer, etc....you get the point.
You can apply for alternative service online and (if you are living abroad) mail any required documents and proof to them in Taiwan before a specified date. The registration period is usually 2 weeks from early April until mid month.