This seems like the story in "The Phoenix Project". If the outsourced software is critical to your operations, it seems it should be brought in-house. Software design is best done when the feedback loop is very tight. It never is with outsourced software.
As for how to go about building a team, you are better placed than I am to figure it out. Probably start with a small team with the most critical bits and build from there.
The old Shipt membership via Target didn't include 2-day delivery without an order minimum. I also don't think having that membership made your shipping orders any faster (only same-day delivery orders), so it seems like an upgrade / expansion as well.