One aspect in favour of the first solution (making the transition as fast as possible, without re-architecture first) is its greater flexibility. You probably c

One aspect in favour of the first solution (making the transition as fast as possible, without re-architecture first) is its greater flexibility. You probably can break down the re-architecture requirement into several parts afterwards. Ideally, you can treat each of these parts as an individual feature having its own priority and put them into the same basket as the other request for new features. You do not then need a master-plan for everything in advance. Instead, you only need to identify the most important feature out of this basket to work on first. After implementing it, the feature basket and its evaluation might have changed, so you can adjust your path in the light of new insights. In contrast, the master-plan approach is probably somewhat faster, if the requirements do not change much during its implementation, because you might be able to cut corners. Since you seem to be rather uncomfortable to choose between the two options, I would take this as a strong indication that you should not miss out on the flexibility provided by the first approach.