Now it's 2085, and human civilization has started to reach the planets. Using the most advanced fission rockets, we can travel from Earth to Mercury in 8 months and from Earth to Jupiter in 1 year. The asteroid belt is now the high frontier, but we are still far from interstellar travel.
Laser or maser pushed lightsail is currently the only propulsion system we can feasibly build to reach a considerable fraction of the speed of light (say 0.25c). However, such a propulsion system emits thousands of terawatts of laser (equivalent to detonating one thermonuclear warhead per second) from its base station, so it can easily be a weapon of mass destruction too, and there will be opposition if someone were to build one.
So the question is, how can a laser-pushed propulsion system be built successfully by a small group, despite the political opposition it may incur? Assume there are no serious technical problems in constructing such a system, and the difficulties are mainly political. To answer this question, you may re-design the propulsion system in any way you see fit, as long as it meets the requirements below. You can also decide who this small group of people is that built the propulsion system.
Technology has been progressing, but humans have not discovered any new law of physics. So by 2085, all new technologies are still based on today's science.
Many nations and corporates are involved in the competition for space, and none can monopolize space yet. No country can assert absolute hegemony on the Earth either. That said, you can't simply eliminate all who oppose you.
The economy in space relies on mining asteroids and collecting solar power. Many powers, primarily chartered companies, focus on scrambling for the asteroid belt. There are some permanent settlements on the moon too, and the moon is mostly under the control of nation-states on the Earth. The development and exploitation of Mercury have just become cost-effective due to the advancements in rocketry, and the competition for Mercury has just started.
The laser-pushed propulsion system will locate in the orbit of Mercury and operate on the abundant solar power there. It also needs a giant Fresnel zone plate located a few astronomical units away from the sun to focus its laser beam. Advanced AIs can mine Mercury and execute the construction project mostly automatically, with little human labour cost.
A thousand-terawatt laser system around mercury will threaten the settlements on the surface of the Moon and cities on the earth (if it can aim and focus its beam on them at all). It can also easily scorch the mining asteroids in the asteroid belt and destroy the surface outposts and the space stations all over the solar system. Therefore, no party will feel comfortable if they know or suspect such a system is built with any military capability, unless it is under their control, or so they think.
Requirements for the answer:
The laser-pushed propulsion system must be able to focus thousands of terawatts of laser in the distance of thousands of astronomical units. It doesn't need to have any ability to serve as a weapon, but such an ability is good to have.
The reason for constructing the propulsion system must be an initiative of a small group of people (and they have the resource to do it). It must not be because of international cooperation or some situation/disaster forcing humanity to do it.
The small group of people who built the propulsion system must not be a secret society, and they must not hold too much power like the fictional Illuminati.
No matter who nominally owns or supervises the propulsion system, the small group of people who proposed to build it must have substantial control over it and can use it for their purposes. (Again, they don't plan to use it as a weapon.) They should also have the power to decide who can use the system.
Optional requirements for the answer: (Try to satisfy them if feasible.)
The construction of the propulsion system should not risk any hostile sabotage or military action to stop it from being built.
The propulsion system should be built openly (you really can't hide something that big) and in a non-threatening manner. It should be advertised as built for exploration and scientific purposes only.
The small group of people who constructed the propulsion system should be private (non-governmental, and not international organizations). But they don't have to be a profit organization.
The construction of the propulsion system should improve the public relation of the small group which controls it, or at least does not hurt their public relations.