Such a range increase makes sense because a SAM has other limitations on its performance including getting to the target directly as quickly as possible but also getting to the target retaining enough energy and speed to perform hard turns without dropping below stall speed.
Other limitations include the performance of the radars being used and the precision the target is discriminated at that range by the ground based radar to get the missile to manouver to occupy the same air space at the same time.
In comparison a ballistic missile just need to gain altitude and follow an efficient ballistic path, so as it gains altitude and travels along its weight gets less and its thrust remains about the same so it will likely get faster as it moves till rocket motor burnout and then it just essentially falls the rest of the way to the target.
Such early missiles were not amazingly accurate and had rather large warheads to help compensate, but also to try to take out more than one bomber with each shot if they were flying in close formation.
The volume of space for the guidance equipment and brain of the missile would free up plenty of space and also reduce weight.
Used as a target drone the SA-2, has a solid rocket booster but its main engine is liquid propellent... the old SA-1 had liquid propellent too, and I suspect they held propellent in storage but didn't keep the missiles fuelled that were in storage, so to use them now they would fuel them up with perhaps more modern and more powerful rocket fuels which on its own should create better flight performance.
There were an enormous number of different SA-2 missile variants, but they have two main training target versions called RM-75MV and RM-75V, the differences are that the RM-75MV is to simulate a low flying target... it can reach 40km range at altitudes of 50m to 500m at speeds of 200-650m/s. The version for higher altitude testing is the RM-75V and it is used at altitudes of 1,000m up to 20,000m, allowing it to reach 40-100km range at speeds of 350-1200m/s.
Of course extending range is not easy... as Iraq found in the 1990s when you extend the flight range of a missile by making it longer and making the fuel tanks bigger the increased flight speed and range put extra strain on the missile... many of the missiles coming in to hit targets in Desert Storm were already breaking up on their own making the job of interception even harder for Patriot which often went for the biggest parts which was often the engine and fuel tank section, leaving the warhead to fall where it might.