ZCTA to Congressional District

Hi all,
I am working with a dataset that is produced only at the zcta level, and I'd like to use that data to create congressional district values. So far I've used the zcta-congressional district relationship file to link the zcta to districts. I've allowed the zcta data to be included in each district it overlaps, so not ideal.

Now I'd like to refine that analysis and split up the zcta data based on the proportion of population within the districts that overlap the zcta (since there are quite a few zcta's that overlap districts). I'm planning a proportional distribution analysis, but wanted to check in here to see if anyone has other recommendations or resources that I could use before diving into that project.

Thanks in advance!