Hiya!
I have plenty of recent diving experience in Egypt, I've done two liveaboards per year from 2021-2024, and a week or two of shore diving each year.
BDE as a diveroute is best enjoyed in late October or early November, in my opinion. That's when it's high season for hammerheads and oceanic whitetip sharks. And possibly threshers at Brothers. Egypt's diving is crowded from June through October, I would say.
My preferred company is
Blue Planet Liveaboards, specifically their boats "Blue" and "Blue Storm". "Blue" is larger than "Blue Storm", but "Blue Storm" is newer. "Blue" has nicer cabins because of her size. Blue Planet Liveaboards also own three other boats: "Blue Planet 1", "Blue Pearl" and "Blue Seas". "Blue Pearl" is also a nice boat, I have never dived off the other two. I have never had safety issues with Blue Planet Liveaboards, the guides have always been very safety oriented in their briefings and in their handling of guests/boats. If a route is deemed problematic because of the weather, the boat manager/head guide will likely present this as a choice to the guests. It happened to me on my first BDE with Blue Planet Liveaboards. The weather was horrible and it would have been difficult to reach Brothers Islands. Darwish told us "Okay, the weather is terrible, going to Brothers is possible but the conditions during the sailing will be horrible, the conditions at Brothers will be horrible, and the last four weeks that we were at Brothers, we saw no sharks. My advice is to sail to Daedalus immediately, skip Brothers completely, and enjoy the hammerheads at Daedalus. But you are the guests and we are letting you vote." So we voted and we went to Daedalus. We were there for 5 days or so because of the bad sailing conditions and the diving was spectacular. If you wish to book with Blue Planet, you can do so through their website which I have linked for your convenience.
I have dived with two other companies in the Red Sea. One was a horrendous experience and I will never dive with them again (they took bookings from guests without having enough beds/bunks for them, the captain made very unsafe diving decisions that led to injured diveguides and guests). I don't want to slander them so I might not name them. The other company is Oceanic Liveaboards. They are "the new kid in town" and my friends' company. Currently, their liveaboards are by invitation-only. They do not own their own fleet but instead hire the newest and most luxurious dive yachts available. Given they're my friends' company, I am mildly biased but their liveaboards are usually spectacular. The boats are truly luxurious, the diving is well-managed and safely executed.
I have never seen any LOB in Egypt that plans on only four divers per DM. Blue Planet usually has 8-10 per diveguide, the other boats that I observed are the same. I would like to add that I prefer to hire a "private dive guide" when I dive with Blue Planet. I don't like diving in big groups either, and one of my friends in Egypt works privately. I usually contact her ahead of time and tell her when I want to come and which route/boat I want. She then contacts Blue Planet, finds an agreement with their owner for her to join as a private diveguide and then someone from Blue Planet emails me an offer and a price. You pay them by transferring the money to their bank account ahead of time. My friend receives approximately €20/day/person in salary as a private diveguide and is well worth her money, especially on BDE. Her salary is directly payable to her, preferably in cash in Euros or Dollars, but she does have PayPal. That way you would be a trio: you, your wife, and her. If you have any more questions, feel free to message me.