I suggest going with the drift test and only the drift test – we have a lot of data correlating it tightly to GET and lactate, but it tends to be more ‘functional’ and is definitely easy to repeat. The above article has all the guidance for the treadmill test and it sounds like you are already seeing it closely track your lactate tests of past. Negative drift usually means the beginning HR was significantly below AeT.
Some folks take more than 15min to warm-up for aerobic workouts, strength, etc. Do what you need to in terms of warm-up.