Maybe I've been lucky, but I've repaired quite a few pendulum clocks by Smiths, Perivale, Enfield and HAC and managed to avoid removing or replacing a mainspring
Complete dismantling is the best way, but if you let down the spring as described and then remove the back cock, crutch and pallet arbor, you should be able to wash out any old congealed oil from the pivots. I use lighter fuel on a modeller's paintbrush as a solvent, then when dry apply some light clock oil. The train should then spin freely when the mainspring is wound up just a few clicks.
Carefully inspect the scapewheel and clean with solvent and paintbrush, then polish the pallet faces with something like 'Bake-O-Bryte' or Greygate Paste Polishing No 5 on a cotton bud. This won't remove heavy wear on the pallets, but if their condition is fair it will help. Remove all traces of polish, lightly lubricate the pallets and reassemble.
Adjust the depth of the pallets' engagement with the scapewheel. This is a trial-and-error process making tiny adjustments of the rear cock each time, with the movement level and the clock running in-beat. What you're aiming at is for the scapewheel teeth to move the smallest distance between the points where the pallets lock them. There will be an optimum point at which the pendulum's swing is at its maximum due to the best impulse from the scapewheel teeth.
All of this only applies as long as the clock is in reasonable condition and the pivot holes aren't badly worn.
Good luck!