What role is the Tyrant supposed to fill?
I just reloaded a fleet battle between AC and Tri-Tach 3 times to test balance. Each time, it was an hour long stalemate. (I didn't actually run it to completion of all reinforcement waves on the 2nd and 3rd attempt.) The Tyrants would prance around and eventually one of them would flank the Tri Tach fleet and kill some epiphanies. They were useless against capitals or even most cruisers because they would jump obscenely far away after sending a single salvo.
Their 4000 armor makes them virtually immune to fighters and most long-ranged guidance missiles--the only kind that could be reasonably expected to hit them outside of player control. The Tri-Tach Paragon was almost never able to connect with the Tach Lance and they would just immediately phase regardless. Massed fighters from the Astral were fairly useless between the 4k armor, the phasing, and the jumping.
25+ minutes into 2 of the 3 fights, the AC managed to have reinforcements kill one of the Astral or Paragon after they were at 0 CR for an extended period of time. None of the Tyrants died. They all retreated safely after my Revenant chased them. My Revenant was also unharmed and never seriously threatened because Tyrants would behave like Wolves and jump away almost immediately.
I made some changes to reduce the jump range from 3,500 to 2,000 and the Tyrant's hull by half. It was still quite durable because of the 4k armor, and would only be killed without retreating when overwhelmed. They were also able to damage my Revenant's hull some in 1 on 1 because of flux pressure from the increased engagement ratio caused by the reduced jump.
If you really did want a battleship to fill a flanking role, my suggestion would be to greatly reduce their peak CR time. They currently jump far enough away not to experience decay a fair portion of the time (which is also why my chasing Revenant was able to stay active for so long), so I'd suggest reducing it by at least half. This would allow them to nom all the Epiphanies, but not draw battles out unnecessarily.
Of course, I've also probably just made Radiants both simultaneously easier to kill and more deadly, but I'd view that as a plus, too.
Sic Semper Tyrannis! Nerf them or make them great again, but please don't leave them like they are.
On the issue of BPs, I found both Tyrant and Malevolent in my AC game last version. I can tell you with great certainty that the critical BP isn't a ship hull at all. It's the Hivemind Orb Launcher BP. Once you find that beauty, you can probably field a fleet of literally nothing but 30 Apogees and... do anything. The only other thing you need is a good book.