Zip Code Heat Map

I have a table Companies that contains the fields company_name and zip_codes. zip_codes contains all the zip codes that they provide service in, separated by commas. Some companies have 300 zip codes.

I want to be able to display a map that shows the areas those companies provide service in, and have it shaded by the amount of companies serving in that area, heat map-style.

Example: Company A services zip codes 1, 2, 3, 4, 5. Company B services zip codes 3, 4, 5, 6, 7. The map should have color in zip codes 1-7, with 3-5 being darker than 1, 2, 6, and 7. 

I've tried doing this with the heat map feature on the bubble map visual, but in order to do this, I have to first separate all the zip codes into separate columns, giving me 300+ columns of zip codes. Going through each one and transforming them into Data Category Postal Code with Don't Summarize is slow and painful, and dragging each of them to Location takes 2 minutes to load each time. 

I've also tried using ArcGIS, but it doesn't recognize multiple zip codes in a value. 

Is there any other way to do this, or do I just have to buckle down and do it the first way that I tried?