A research lab has developed a powerful, general-purpose language model pre-trained on a massive corpus of text from the internet. They now want to adapt this model for a niche medical task: classifying patient notes into five distinct diagnostic categories. The lab has a high-quality, but very small, labeled dataset for this task and limited computational resources (i.e., budget for GPU time). They are debating two adaptation methods:

1. Method A: Update all of the model's parameters using the small medical dataset.
2. Method B: Keep the core language-understanding part of the model fixed, and only train the final classification part of the model on the medical dataset.

Which method would you recommend for the research lab? Justify your choice by evaluating the primary trade-offs of each method in the context of the lab's specific situation.