The Planck scale, where quantum gravity should have directly observable consequences, is ~10^18 GeV. The world's most powerful collider to date, the LHC, reaches a collision energy of ~10^4 GeV, not far from the theoretical maximum attainable by a ring of its size [1].

If you wanted to scale up the LHC by an energy factor 10^14, you would have to deal with the energy loss caused by synchrotron radiation (charged particles going around a ring are constantly accelerating, so constantly emitting electromagnetic radiation) which is ~E^4/R per turn [2]. To keep the same energy loss as at the LHC and pay an electricity bill which is only 10^14 times larger, you would therefore need to grow the radius R by a factor ~ 10^14^4 = 10^56.

The LHC radius is 4.5 km, so let's go with R = 10^56 km. That's 10^43 light years. For comparison, the radius of the observable universe is ~10^10 light years.

[1] http://www.physics.princeton.edu/~mcdonald/examples/lep.pdf

[2] https://arxiv.org/abs/1504.01627

[3] https://en.wikipedia.org/wiki/Observable_universe#Size

A linear collider would not be long enough. A circular collider would need either unattainable magnetic fields to curve the trajectories of the particles or itself have curvature that is small enough (i.e. have a radius similar to that of Earth's orbit around the Sun).

So yes, it is really unattainable.

Cosmic rays bombarding the atmosphere do attain such energies, but they are not controllable in a fashion that would permit most collider experiments.

All our manipulation of particle trajectories use electromagnetic forces.

If we were to be able to come up with the technology to manipulate the strong force, would that open up possibilities for alternative colliders?

One problem that I can see is that the strong force might be stronger (strength of 1 vs 1/137 of the electromagnetic force) but the acting range of the force is much smaller (diameter of a medium sized nucleus). The electromagnetic force has a far superior range (technically infinite, but the power drops off depending on the distance)

Arm chair physicist here... I would love your knowledge on the general idea.

Could something be built in space?

Theoretically, yes. If you set up billions (maybe even trillions) of powered electromagnets in a stable, very precise orbit around the sun and injected particles into the loop. However, this is hugely impractical and the sources of error would be huge. Electromagnet misalignments (with the error compounding over stellar distances), stray asteroids and comets, cosmic rays, etc would all effect the particle beam.

How much money are you willing to spend? ;-)

One way is to probe them indirectly. For example, string cosmology makes testable predictions (verifiable by observation, e.g. of the CMB). Conceivably, evidence could be found of something that happened in the early universe that is most easily explained within the string theory.

If memory serves, I believe a collider with a diameter the size of a galaxy would be needed to accurately test string theory. This isn't to say that we won't come up with some alternative method of producing high energies though.