the King Jaguar is not going to be too likely to meet its match since the larger Orion ships don't seem to be as good a deal for the point values, so I'm more likely to meet a larger number of medium-sized (and very deadly) Orion phaser boats.
The king jag is the equivalent, points wise, of 2 orion LRs with ph1s. Not sure I fancy the Orion chances there, they suffer the same problem most such situations have - a larger ship can concentrate on 1 of the smaller ships and quickly take out the lower shielded more fragile ship. The LRS have 12 ph1s, the same as a BC for exactly the same points, though they lack the Ph3s.
Power wise, Both sides can do speed 24 and fire all main weapons on non-battery power, the KJ can also do speed 16 fire all main weapons and fully battery 2 volleys a turn on non-battery power, the LR cannot quite do that. The LR can double engines, but loss of stealth and self inflicted damage just compound their fire power disadvantage.
If the orions settle for a range 9+ engagement then they will lose. If the KJ gets to range 0 or 1 it can easily blow away one LR , and can muster enough firepower to (theoreticaly) wipe out both LRs in one go with just average damage. The LRs on the other hand usually won't even cripple a KJ at range 0 with all 12 ph1s.
The LRs have a clear turning advantage, but that is all they have to offset the Lyran advantages. I don't see the larger Lyran being clearly overwhelmed by multiple smaller Orion vessels.
In effect, the BR seems to be where they peak as far as point value efficiency goes
In terms of ph1s The BR is less points efficient than a BC (by a fraction).
I dare say that different races see different changes in ship efficiency as they get large, but looking at klinks, as that was one of your complaints earlier.
Upgrading a Br to a BC adds 3 ph1s (capable of forward fire), 2 shield and 19 total extra boxes, whilst a D5 to a D5W gets 2 extra ph1s and upgrades 2 (back end) ph3 to ph2 and 16 total extra boxes.
I don't see an obvious decrease in efficency there relative to the klingons. I'd say they are about the same.
and smaller Lyran ships - with many PH-2s - can't quite match up to them.
The lyran doesn't have a BR equiavalent, but droppping down to a Double raider you are looking at a Lyran Alleycat. The Orion looks a monster with 8 ph1s and 4 ph3, but it is under powered compared to the alleycat (unless you start doubling), and they both have the same turn mode. The Alleycat can do speed 24 fire all main weapons and have a point of power left for battery. At longer ranges there is not much difference between a Ph1 and a Ph2 vs stealth (average 0.5 to 0.33). The Orion has to surrender move initiative (and go slower) just to stay equal with the alleycats long range damage. At close range the lack of a turn mode advantage means the Alleycat is more likley to get those ESGs in, if he does then it is, more or less, good bye Orion. The orion has the firepower advantage in the 3-8 ranges, but the power difference could make that hard to take adavantage of. The Alleycat could just dispense with long range and hit speed 32 whilst under EM with power for batteries and repair the odd point of damage he takes in shields. The orion just can't out run him whilst outshooting such a ship, and presumably at some point hits a map edge stopping him outrunning either. Both sides have some advantage they can use, but overall they look to stack up in favor of the Lyran to me. Or at least I'm not seeing an obvous lost game for the lyran.
I like orion phaser boats and their flexibility in the tourney style game where you can't be sure what you will come up againt. But I am not seeing your argument that the Ph1 boat is overpowered, either generally or even at the smaller/medium end.