Chatbots or conversational agents (CAs) are increasingly used to improve access to digital psychotherapy. Many current systems rely on rigid, rule-based designs, heavily dependent on expert-crafted dialogue scripts for guiding therapeutic conversations. Although advances in large language models (LLMs) offer potential for more flexible interactions, their lack of controllability and explanability poses challenges in high-stakes contexts like psychotherapy. To address this, we conducted two studies in this work to explore how aligning LLMs with expert-crafted scripts can enhance psychotherapeutic chatbot performance. In Study 1 (N=43), an online experiment with a within-subjects design, we compared rule-based, pure LLM, and LLMs aligned with expert-crafted scripts via fine-tuning and prompting. Results showed that aligned LLMs significantly outperformed the other types of chatbots in empathy, dialogue relevance, and adherence to therapeutic principles. Building on findings, we proposed ``Script-Strategy Aligned Generation (SSAG)'', a more flexible alignment approach that reduces reliance on fully scripted content while maintaining LLMs' therapeutic adherence and controllability. In a 10-day field Study 2 (N=21), SSAG achieved comparable therapeutic effectiveness to full-scripted LLMs while requiring less than 40\% of expert-crafted dialogue content. Beyond these results, this work advances LLM applications in psychotherapy by providing a controllable and scalable solution, reducing reliance on expert effort. By enabling domain experts to align LLMs through high-level strategies rather than full scripts, SSAG supports more efficient co-development and expands access to a broader context of psychotherapy.