Adaptations of Transformer models, such as BERT4Rec and SASRec, achieve state-of-the-art performance in the sequential recommendation task according to accuracy-based metrics, such as NDCG. These models treat items as tokens and then utilise a score-and-rank approach (Top-K strategy), where the model first computes item scores and then ranks them according to this score. While this approach works well for accuracy-based metrics, it is hard to use it for optimising more complex beyond-accuracy metrics such as diversity. Recently, the GPTRec model, which uses a different Next-K strategy, has been proposed as an alternative to the Top-K models. In contrast with traditional Top-K recommendations, Next-K generates recommendations item-by-item and, therefore, can account for complex item-to-item interdependencies important for the beyond-accuracy measures. However, the original GPTRec paper focused only on accuracy in experiments and needed to address how to optimise the model for complex beyond-accuracy metrics. Indeed, training GPTRec for beyond-accuracy goals is challenging because the interaction training data available for training recommender systems typically needs to be aligned with beyond-accuracy recommendation goals. To solve the misalignment problem, we train GPTRec using a 2-stage approach: in the first stage, we use a teacher-student approach to train GPTRec, mimicking the behaviour of traditional Top-K models; in the second stage, we use Reinforcement Learning to align the model for beyond-accuracy goals. In particular, we experiment with increasing recommendation diversity and reducing popularity bias. Our experiments on two datasets show that in 3 out of 4 cases, GPTRec's Next-K generation approach offers a better tradeoff between accuracy and secondary metrics than classic greedy re-ranking techniques.