iPhone 6 Plus Battery Draining after Screen Replacement.

This is a belated answer so hopefully it can be of use to folks who search for and find this question.

Sometimes the replacement parts we receive can be defective or partially defective. Some vendors have better parts than others and generally speaking, you get what you pay for. Did the replacement screen come with the Front Camera and Sensors pre-installed or was it just the screen?

Potential problem areas with replacement screens:

1. If the backlight on the replacement screen is not at the proper spec or defective, then it can cause excessive current draw and cause faster battery drain.
2. If the FCAM/Sensor is partially defective (assuming a full assembly), it too can draw excessive current.

The best way to eliminate some variables is to put back the original screen to see if the problem persists. If it does, then the problem is at the logic board level (damaged connectors, pry damage etc.). If it doesn't then something about the replacement screen is causing the issue. You could then disconnect the FCAM/Sensor and Home Button to see if the problem goes away.