When making up prayers for an entire year due to not performing ghusl after masturbating, must I intend to pray according to the order of the day and month, or should I intend to pray only according to their known order?

Ghusl (definition) is only obligatory if you are absolutely certain that semen, which necessitates ghusl, has been discharged. If there is doubt, ghusl is not obligatory. Assuming you are certain of semen discharge, there is a scholarly difference of opinion regarding the obligation to re-perform prayers that were offered in a state of impurity due to ignorance. If one holds the view that re-performing them is obligatory, then the necessity of maintaining sequential order among missed prayers is also a matter of scholarly difference. The Shafi'i school does not consider it obligatory, unlike the majority, and this is a strong opinion. If one holds the view that sequential order is obligatory, then you begin with the first prayer you missed, performing it and those thereafter in order, until you have completed all that is due from you. You should only abandon the sequential order if you fear missing the current prayer's time.