Overload range is 6", not 8", so if you can end up at 8" he can't overload on you.
Believe me, I thought the Klingons were way overpowered the first few games as well. I took the advice of more experienced players and just dove in there for a close range fight (try to be over 4" away to keep all those Phaser-2s out of Kill Zone). He can't keep his front shield pointed at all possible enemies if you swarm him at close range. Flank him as much as you can.
Also, it may seem counter-intuitive, but if you have the choice of a closer target but he's pointed his front shield at you, or a slightly worse shot at a Klingon's flank, take the longer flank shot. You'll do double the damage. Otherwise you waste nearly half of your damage against that front shield.
Another trick that works vs the Klingon double shield rule is to not fire all your weapons at once. Fire by weapon system, one by one, until the shield drops. Also remember that if you hit with 2 1-pt phasers, they are halved to yield one hit, but if you split fire with your weapon systems on 2 targets, each one takes one point of damage (1 hit halved but rounded up). Thus if you have 2 worthwhile targets in arc and they are both pointing their front shield at you, and you have a 2 dice Phaser-1 battery, split the dice up and fire one at each target. This yields one hit on each target. If you'd fired both at one target and hit with both, those 2 points of damage are halved (ie, one point is wasted).
If you let him play his game, which is keeping you at medium range and in front of him while he pings your shields away, you lose. Get in there close, and hit him on the flanks and watch the smaller-hulled Klingons burn.
I'm at about 60/40 Klingon/Fed win loss ratio, so I still have some work to do figuring out tactics, but the first 5 games, the Klingons won 100% of the time. Once I started to dive in there and get more flank shots, the win ratio started to go more my way. That reminds me, do pay attention to the suggested map size in the rules. Larger maps give the Klingons too much room to maneuver and they seem to win more often on larger maps. Try a 3'x3' map, maybe with some terrain.