"Would it be possible to partially measure the entanglement and use out the conservation of energy to transport energy from one place to another while preserving the entangled state?"
Whoa there, Geordi. Cool your tachyons. Let's deal with this more basic assumption first before we go all quantum...
"You can't carry around energy-dense things on the battlefield, cause the denser they are in energy the higher the risk of explosion, thank it to the fundamental rules of the universe."
...except for all the fuel, gunpowder, and explosives everyone carries around with them on the battlefield. And the liters and liters of gasoline we drive around with.
Let's deal with the assumption that "energy density == explosion". Hollywood would have us believe that EVERYTHING EXPLODES!!! Especially cars and sci-fi consoles. Reality... not so much. Energy density != explosiveness.
For example, gasoline and other hydrocarbons have some of the highest energy densities of any non-radioactive material, about 47 MJ/kg. Unlike what you see in the movies, gasoline is very hard to ignite. Gasoline must first be vaporized and mixed with air before it will ignite, this is why a thin film of gasoline will ignite, but drop a lit match in a bucket of gasoline and it will go out. This is why some cars are fitted with special fuel tanks that collapse as they empty to avoid having a bunch of vapor in a half-empty tank. This is also why we're allowed to drive around with 1.4 GJ of energy (40 L of gasoline @ 0.73 kg/L is about 29 kg) in our fuel tanks.
In contrast, explosives like TNT and gunpowder have a fairly low energy density, about 4 MJ/kg. We use them as explosives because when they ignite, they detonate which means they combust so fast there's a supersonic shockwave of expanding gases. A gasoline or black powder explosion is, in contrast, pretty slow.
We also use those particular explosives because they're very stable. Most require a detonation by a small amount of unstable explosive to themselves explode. For example, gunpowder is touched off by a small primer of mercury fulminate which can be set off by the hard shock of being struck by a firing pin. Whereas C4 explosive is so stable it can be shot, hit with a hammer, burned, and microwaved. It requires a detonator, a supersonic shockwave, to explode.
The question isn't how energy dense an object is, but how stable it is. Fissile materials like uranium and thorium have an energy density of 80,000,000 MJ/kg, but without a lot of work it's just a radioactive rock. Hydrogen has an even higher energy density if you put it into a fusion reactor.
And no, fusion reactors (probably) don't explode. A fusion reaction requires very high pressure generated by a magnetic field, otherwise the high temperature plasma simply blows itself apart in a small puff of hydrogen (you don't need a lot of mass in a fusion reactor). Once the magnetic containment fails, the pressure is released, the gas expands, and poof the reaction stops. You can also make fission reactors which are "passively-safe" meaning by its very nature it will shut down safely.
Your solution is to come up with a device that is very energy dense, but also very stable. If you're talking warp drives and plasma guns, I'm going to say a micro fusion reactor.