Workshops might not be required in this case, but if they're feasible, they're helpful. Bringing together several people who know something about each customer persona, talking through each experience in detail, can supplement what the customer experience research team has identified.
One approach you might want to explore is as-is scenario mapping. Prior to the workshop, you'll send out the current-state scenarios you'll define together (such as "As a leisure traveler, I want to start exploring the best prices for my upcoming vacation"). You'll share the persona data with the team ahead of the workshop, too, so that everyone will have informed assumptions.
In the workshop, the team will map the scenario using stickies to define what each customer is doing, thinking, and feeling. The link above has more information on the exercise.
You can then use each scenario (as a phase, if it makes sense) to create end-to-end experience maps for each persona, which is helpful because it'll surface the high and low points of the experience in a nice way. There are several examples available online, in varying levels of detail.
Once you've mapped the current state, it becomes easier to brainstorm the future state journey that you'd like to envision.
I recommend reading UI Is Communication by Everett N. McKay, which has chapters on personas and journey maps that are coincidentally specific to the travel industry.