Alex90, beautiful guitar you have there. I recently picked up a N.O.S. 2020 ESP/LTD H-1001, so mine is fairly similar to yours. Did your guitar originally come with a Pegasus bridge, along with that Sentient? Mine did, and I'm changing the bridge pickup to a Black Winter, while keeping the Sentient.
What I discovered, unfortunately after buying the Black Winter replacement, is that LTD only routed their bridge pickup cavity deep enough for the Pegasus. So the choice became, find another pickup, or route the cavity deeper. I really like the Black Winter, plus it's silly that a guitar company wouldn't have the foresight that an owner may want to change pickups at some point. I had installed the Black Winter but it was
way too high, almost touching the strings, and as far as adjustment it was already bottomed out. Plus it sounded like crap with the pickup set so high. So I took the Black Winter back out, temporarily.
Here's the important point: I still have an EMG set from a different guitar, so I checked their overall height (from bottom of the mounting tab, or "leg." to the top of the pickup), and they are identical. So I suspect that you'd need to route your pickup cavities deeper to accommodate the EMGs.
I chose to route the bridge pickup cavity deeper, because I didn't want the guitar to limit me for any future pickup changes, and/or to install the Black Winter. (I'll be reinstalling the BW hopefully today.)
That being said, from what I understand active pickups can be closer to the strings than passives, so you may still get away with the EMG installation anyway- but I wouldn't be too sure.
Hope this helps!