I understand the need to pottytrain on a deadline for a similar reason to your own! My DD had to be pottytrained by age 3 to go into the 3-year old class at preschool. Otherwise, she would have had to remain in the under 3 class with kids as young as 20 months and she just did not share the same interests with that age group anymore.
I will preface what worked for us with the fact that my DD had shown previous interest in pottytraining and had gone on the potty a few times as well as could hold it for a long time, knew when she had to go and would hide to do her business and all of the other pottytraining signs plus, frankly, was smart enough to know what to do.
We tried everything we knew to try after her initial interest and readiness signs. We did a reward system where she got to pick a prize, we made her sit so many times per day and made a big deal about the whole thing, we stopped talking about it completely to see if it was just too much pressure, etc. You name the theory - we tried it.
Finally, it was late June and she was to start school the second week of September (which is also the week of her third birthday). I was starting to panic as I only had 2 1/2 months to get her completely trained. I did some research on the internet and finally read some stuff that made complete sense to me.
With my smart, precocious DD it was essentially a power struggle and that she needed to have the power. So, we gave her the power but under our terms as suggested by what I read. We did two things. One, I bought something I knew she would love. I told her it was mine and that I would let her use it for 30 minutes every time she went to the potty. In her case, it was a new princess dress. I don't think this is what did it for her but thought it was important to include as part of the process. The second thing we did was find a long weekend that I knew we would be with her the whole time and did not have a lot planned. We chose the 4th of July long holiday weekend. Then, we told her that she was no longer wearing diapers. We informed her that she would be wearing underwear from now on. Then, we gave her the power and told her that it was her choice - she could either go on the potty or she could go in her underwear and on the floor. If she chose to go on the potty, great. If she chose to go in her underwear and on the floor, that was fine too but she had to help clean it up. This gave her all of the power and choice. She peed once in her pants and on the floor and helped to clean it up and once in her pants and outside on the ground since we were not at home and she did not want to pee on the potty. That was it! She decided she would rather go in the potty than deal with the feeling and mess and was completely trained in a day and a half that weekend! She had very few accidents afterward and only wore nighttime pullups for a little while.
Sorry I got so long-winded and wrote a novel but I wanted you to know others have been in the same position and what worked for us.
Good luck!