Thank you for your post.
The more keys added to a relationship, the more evaluating it needs to do. Previously, your calculated key makes one reference and is easy to look up. Now, it looks up four different criteria.
It shouldn't be that much slower. I have one table with five keys, and the result is fast (< 1 second with 25000 records). Then again, I don't change the keys, and I don't have a range for Start Hour and End Hour. If you modify the key, then it has to calculate the relationship again and link to the appropriate records. You may want to consider combining two of the equality fields (instead of the date fields that use "less than" and "greater than" operators). This may help with the speed.