Yes they get toasty quick. I have a tour pearl and it goes too long in the particular situation. They are simply drilled completely differently. May need to consider the hyroad option.
I would go to an Asylum, but with a smoother cover than box. A true 4000 grit finish, or possibly storm step #1 rubbing compound would be good options. This would bridge the gap between your Tour pearl and Crux.
I usually try to stay away from recommending to use a solid as a step down from a hybrid. It's one thing if you are starting with a solid, and ball down to a weaker solid, but if you are at a low Rg high diff asymmetrical ball like the Crux, than a low to mid Rg with medium to high diff symmetrical but still a hybrid is a better way to go, at least in my opinion. The other option would be to go with a Fusion, with a slight bit of surface. The Asylum is one of the most under the radar, under-rated balls on the market today. It takes changes to the cover easily, and has a wider pattern coverage than a lot of balls on the market today.
Another option that would also be a step down from your Crux, but stronger than your IQ Tour pearl would be the Byte. The Byte would still give you a more defined shape like the Crux, but will not slow down as early, and give you more push down the lane.