Thanks for the reminder about the track photos - that's a good size track, about 5ft longer than the track I set up at home. I don't need to use jumpers on mine.
I think you've narrowed down the issue. I'd still be tempted to isolate the LCs from the big track in a small oval with the powerbase. I think that would set your mind at ease that the LCs are functioning correctly on their own. And you could test them straight after a corner and see if there any issues. However, with a variety of cars, I would expect only some cars to miss the sensor, not all. Most should get through at low speed and if manually pushed over the sensor. I did notice that you can move one lane changer a 1/2 straight away from the corner. I'd be tempted to do that.
The power drop is the main cause for concern. Almost any track - designed in software or built freehand - won't join up perfectly. The Scalextric track does allow for some flexibility (unlike the more rigid HO track pieces, plus Carrera etc) and with a bit of 'jiggling' a small-ish gap should be easily swallowed up. A 1cm gap should be fine. However, that jiggling needs to be done right around the track - a 1cm gap spread over 20 or more track joins is nothing. Closing a 1 cm gap at one track join might cause problems.
One thing I would check is that the plastic tabs at the track joins are locking tight. Sometimes - especially with new track - the tabs don't lock. If that's the case, lift the little 'locking' tab upwards...
If you can identify exactly where the power drop begins, that will help you find the problematic track join. If you temporarily disconnect the track from the right-hand side of the powerbase, you'll probably get a dead stop where the problem is - or at least a more pronounced drop.
Good luck