I agree with you that you probably need to lift the base of the rear seat. I can't test this myself as my seats are folded down and the resultant space is lined with wood. This thread provides some reassurance.
However, due to an earlier query on this forum I have found a Youtube video that shows this (although it skips over re-inserting the seat belt ends when the base is replaced!). https://www.youtube.com/watch?v=lSLm1O42-jg&t=5s Go to 4.20 to see the relevant section. You may need to use more strength than you initially expected to lift the seat. Access your inner mechanic