A small increase in surface gravity may be enough... quite how big an increase depends on the tech-levels you're prepared to work with.
The problems increased gravity causes are twofold.
Firstly, orbital speeds. The velocity of a body in a circular orbit around a planet is $v \approx \sqrt{GM \over r}$ (where $G$ is the gravitational constant, $M$ is the mas sof the planet and $r$ is the orbital radius, measured from the very centre of the planet), which you can use to see that at 200km above Earth your orbital velocity will be about 7.78km.s. Assuming that your 1.5G Superearth has the same average density as the Earth, orbital velocities for the same equivalent altitude will scale by about 1.5x.
Any rocket launching from your world will need to boost itself to a velocity of 11.68km/s. Most problems in rocketry boil down to the rocket equation, which can be written as $\Delta_v = v_e \ln{\left( m_0 \over m_f \right)}$ where $\Delta_v$ is the rocket's maximum change in velocity, $v_e$ is its exhaust velocity, $m_0$ is its initial mass when fully fuelled and $m_f$ is its final mass when all the tanks are dry.
Given the same rocket technology as Earth, $v_e$ will be the same on Superearth but to increase $\Delta_v$ by 50% you need to increase the rocket's mass ratio by ~1.65. This means that without increasing the weight of any other component, the rocket needs to carry 65% more fuel on Superearth than it would on Earth. That's a big engineering problem in itself... you could throw on extra stages to your rocket, but it'll be awkward engineering and the amount of rocket needed to put a tiny object into space will be huge as will the costs.
The lower stages of the rocket will need 65% more thrust in order to maintain the same level of acceleration on the now much-heavier rocket... and on top of that, it needs an additional 50% more thrust than the same rocket would on Earth simply to overcome the greater force of gravity!
Rocket thrust is defined as $F = \dot{m} v_e$, where $\dot{m}$ is the mass of fuel you're throwing through the engine per second, and $v_e$ is the exhaust velocity. If you keep the same $v_e$ (eg. you use the same chemical rocket technology as we do on Earth) you have to increase $\dot{m}$. You can do that by adding more rocket motors (expensive, complex, more things to go wrong) or bigger rocket motors (more expensive, differently complex). You're also faced with the issue that you have to burn your fuel much faster to feed those new engines, and so in order to not run out of fuel you need to carry much more of it, which needs a bigger rocket with bigger engines to lift it... you can see where all this goes.
Chemical rocketry just isn't going to cut it here. You need something which has a much high exhaust velocity $v_e$, and that means you need nuclear rockets.
Increasing exhaust velocity by 50% using nuclear power seems entirely possible... even the simplest design, the Nuclear Thermal Rocket (which has been tested in real life, but never flown) can manage that. Having a high enough thrust-to-weight to get off the ground is a bit more challenging, but might still be possible. In the limit you can always reach for Project Orion. Such a vessel might even be able to take off from the surface of a 2G world, though the amount of nuclear warheads it would need to carry and the amount of fallout it would generate would be... alarming, and certainly cause political issues.
I suspect that your people might well remain ground-based until they devise a working laser launch system. A sufficiently powerful laser launcher is certainly beyond our current technological capabilities, an if your Superearth has a particularly thick atmosphere it'll be even more challenging for its inhabitants. Not necessarily impossible, though!
So, to cover your specific observations:
More efficient fuel is too dangerous to handle.
More efficient fuel is rare or very hard to mine on this satellite.
Nuclear fuel isn't that dangerous, but it might be entirely absent on your gas giant moon. If your moon formed far enough out in its planetary system, it will be high on water, but low on metals and maybe uranium and thorium is all but absent.
The acceleration needed to reach escape velocity would kill anyone inside the rocket/launch loop/exotic propulsion device.
Probably not. Acceleration could be surprisingly low, with a clever enough launch system.
The atmosphere itself impedes rocket launches.
A Venusian-style thick atmosphere would be a bit of a killer for surface launches, but you might be able to build high altitude balloons, as Landis envisaged, and build your rocket launch sites up there. It will not be enough by itself, but combined with high gravity (and indeed, higher gravity seems likely to get a much thicker atmosphere) it would certainly make things harder.
