First, congratulations on your Synergy E7SE purchase. It is a well designed and sexy helicopter.
Lets go over a few points.
1) Seller issue: Unless the seller had warned you about the damaged components, he should take responsibility for these damaged components and compensate you accordingly or even accept the helicopter back for a full refund. Inspect and scrutinize each component very carefully before rebuilding.
2) HV Servos: HV servos are generally designed to handle the voltage of a fully charged 2S LiPo. That is 8.4V. Your BK and MKS HV servos will handle direct connection to a 2S LiPo without issues. When I discussed this issue with Tomas (MKS USA distributor), he advised me that exposing HV servos to voltages above 8.0V for the majority of their lives will reduced its potential lifespan. Using a 2S LiPo does not seem to be an issue as the voltage quickly drops during use to around 7.8 to 7.9V, which seems to be a good compromise between optimal performance without significantly affecting useful life.
3) CC BEC Pro: That's the same BEC I used on my E7SE. I powered it with the first 6S LiPo of the flight pack series. I set the voltage to 7.5v. I never ran into issues with this setup. Knowing what I know now, I would have increased the voltage to 7.8v to 7.9v for optimal HV servo performance. Although I never ran into issues with it, I would also consider using one or two
4.7uF capacitors (or an
R2 Buffer Super Capacitor) connected to either the receiver and/or FBL unit empty port(s) for added voltage smoothness.
4) 3S LiPo: If you are planning on using a separate LiPo to run the electronics, I consider a straight 2S LiPo a more practical option that the 3S LiPo connected to a BEC like you are considering. One of the main reasons to use a BEC is to eliminate the need for a separate battery. If you are planning on using a separate battery anyway, you would be defeating the value of a BEC. If you are intending on using an external BEC, consider connecting it to your main packs. If using the CC BEC Pro, connect it to the first 6S pack in the series (do not connect it to 12S). For the ultimate wire neatness, consider using an ESC with a known robust internal BEC like a HobbyWing V4 ESC.
Best wishes on your rebuild.