That's a very great question and a popular scenario in for most of product base companies. I hope my suggestions are relevant to your situation.
In a redesign process, you should first understand what is your motivation to do the redesign. If it's a brand updates and all other marketing concerns, that's a different scenario. But if you are concerned about your users, I believe you should consider contacting your users first. Having a solid data base of user feedback and user pain points would be absolutely useful for the future of your redesign process. You also need to keep everyone in your meeting aware of the business goals and all the annual plans so they can have a little bit of focus in their design ideation process.
In your case I would encourage you to first try to find user feedback from your internal system, the customer service department could be a great help in these kind of situations. Let those half of your team members who know about the product to be aware of those user feedback. Then in your meeting, ask the other half who don't know about the product to start using it and critiquing what they see and discuss it with those half who know about the product and also all other user feedback. That way you get a good understanding of what are the major pain point and also at the same time you will be helping all of your team members to be familiar with the ins and outs of the product. This exercise may take up to 30 minute of you 90 min meeting.
Then I would highly recommend to do an empathy map with the whole team involved. That makes everyone to be in a same page about what are user actions, feelings and thoughts while they are in a major scenario that your product will be an option to be used. There is actually a great template in one of the articles in UXmastery and it would be nice to let your team read that before the meeting. (this exercise shouldn't take more than 20 minutes)
Now it's time to analyze the product. What I would recommend is to have your UX journey plotted on a large size and let the team look at that considering the empathy mapping experience that they just have finished. That really helps you to understand the pain points and define the right problem statements that need a redesign. Once you have the pain points listed, you have all the talents in your team, ask them to be in 3-4 team and start sketching and come up with creative solutions for those pain points and problems. Then at the end of this meeting you have several problem statements ready with a lot of great potential solutions for them to be presented for your stakeholders and business owners.
I hope this helps...