If the WW clock was mine, I'd be sure the cord was not fowling on the winding spool and wound evenly in a neat spiral without overlays.
Next I'd substitute a lighter weight on the timekeeping works. It may be that the movement isn't as free of binds as you were led to believe. One little caveat: if the pillars are loose in the plates, then a lighter weight won't pull the plates out of square as much as a heavy weight.
Next, I'd remove the strike weight to see if there's a fault with the strike release linkage.
Another thing to try is to let the clock free run without a pendulum; just the crutch. Alternately, remove the verge and control the movement by pressing on the 'scape wheel arbor.
But since I have a MicroSet timer, I'd hook it up to the clock and record the clock's performance on a lap-top computer. Program the MicroSet to time double the number of teeth on the 'scape wheel. The resulting accumulated graph could pin-point a swolen wheel or a bent pivot. Cyclic flaws in the wheel train become very evident on a MicroSet graph recording.
Les