In this paper, several iron-free solenoid-based designs of a detector magnet for the future circular collider for hadron-hadron collisions (FCC-hh) are presented. The detector magnet designs for FCC-hh aim to provide bending power for particles over a wide pseudorapidity range (0≤|η|≤4). To achieve this goal, the main solenoidal detector magnet is combined with a forward magnet system, such as the previously presented force-and-torque-neutral dipole. Here, a solenoid-based alternative, the so-called balanced forward solenoid, is presented which comprises a larger inner solenoid for providing bending power to particles at |η|≥2.5, in combination with a smaller balancing coil for ensuring that the net force and torque on each individual coil is minimized. The balanced forward solenoid is compared to the force-and-torque-neutral dipole and advantages and disadvantages are discussed. In addition, several conceptual solenoid-based detector magnet designs are shown, and quantitatively compared. The main difference between these designs is the amount of stray field reduction that is achieved. The main conclusion is that shielding coils can be used to dramatically reduce the stray field, but that this comes at the cost of increased complexity, magnet volume, and magnet weight and reduced affordability.