Greg, If you like the color Ipe, then at least cut the ends out of cross grain, so it matches the substrate. Your failure is due to the grain direction being opposite more than anything else.
The inlay doesn't have to be one long strip, but can go in as little short pieces cut from any solid plank, so you don't have to worry about handling a long fragile strip breaking before you can get it glued.
You could improve the epoxy bond by running down the bottom side of your inlay strip with a right angle disk sander with coarse 24 grit before you rip them off. This will give the epoxy some tooth to hold onto.
You don't mention whether you thicken the epoxy, but most epoxy is brittle when used straight, but you may be able to get something to add into the mix to make it more flexible too. I always add some silica to thicken when using it as an adhesive. I add some dust from my portable belt sander bag to that to get the color I want.
Quality control is usually a good practice. You could cut some wide thin cross grain strips of both species exactly the same length, then zap them in the microwave to see how much they shrink for comparison.
But let me be clear, since you posted this in the adhesive section. Your failure wasn't due to the glue. If it had not buckled and popped out, then the table would have split which to my thinking would be a bigger problem.
Running the Ipe cross grain may not be all it takes. A less dense / more easily crushed like mahogany might make a better wood choice. It is also easy to stain or dye to get good color.
Good luck