Carpet shouldn't be a problem with that setup. It stretches over imperfections well.

Another option is vinyl planks. They might charge more for the extra effort, but a smart contractor should know how to handle putting planks over the ramp. I've done a similar job when I was 19. I cut the plants flat to the edge of the ramp, then cut a slight angle for the ones over the ramp. Just had to cut the moulding a bit higher but it fit fine. If your husband is a confident DIYer he might be able to figure it out himself. Shouldn't need much more than a slight angle saw for the cuts.