Okay, so the size is not the issue for sure. Have you re-created the index table after selecting the custom fields? Although that does not explain the problem, why there are only non-partial matches.
If you create a completely new search bar for testing, select the desired post types only and switch to the index table engine, does the problem persist? If not, then there is a configuration issue somewhere.
Maybe there is a generic filter enabled for the exact matches, make sure there is nothing selected: https://i.imgur.com/JcjI0xh.png
The filters do have effect even if they are not visible.
