When you take the approach of developing mental multiplication skill to address the need for solving problems listed in the times tables, it is really helpful to develop a strategy of identifying the fastest (normally the easiest) route to solving any particular multiplication problem. By doing this at outset, the steps required to arrive at the final answer to the multiplication problem are much easier to handle, and can often be run through at a speed similar to that with which rote-learning students are able to recall the answers from memory.
With practice, the speed difference can be so negligible that any observer may think that you are recalling answers from memory, and certainly with greater confidence in the accuracy of answers.
One of the problems with most method-based approaches to the times tables is that each method (e.g. the 'fingers' method for the nines) is that each individual method solves part of the overall table of multiplication problems, but that the rest of the table needs to be covered by other individual methods. A fully comprehensive approach, however, addresses the times tables entirely, without leaving any gaps.