Current machine learning techniques for dementia diagnosis often do not take into account real-world practical constraints, which may include, for example, the cost of diagnostic assessment time and financial budgets. In this work, we built on previous cost-sensitive feature selection approaches by generalising to multiple cost types, while taking into consideration that stakeholders attempting to optimise the dementia care pathway might face multiple non-fungible budget constraints. Our new optimisation algorithm involved the searching of cost-weighting hyperparameters while constrained by total budgets. We then provided a proof of concept using both assessment time cost and financial budget cost. We showed that budget constraints could control the feature selection process in an intuitive and practical manner, while adjusting the hyperparameter increased the range of solutions selected by feature selection. We further showed that our budget-constrained cost optimisation framework could be implemented in a user-friendly graphical user interface sandbox tool to encourage non-technical users and stakeholders to adopt and to further explore and audit the model - a humans-in-the-loop approach. Overall, we suggest that setting budget constraints initially and then fine tuning the cost-weighting hyperparameters can be an effective way to perform feature selection where multiple cost constraints exist, which will in turn lead to more realistic optimising and redesigning of dementia diagnostic assessments. Clinical Relevance-By optimising diagnostic accuracy against various costs (e.g. assessment administration time and financial budget) predictive yet practical dementia diagnostic assessments can be redesigned to suit clinical use.