if it flushes fine using a bucket on solids the drain is NOT a problem.
plunge as much water out as you can, sponge the remainder from the bowl.
insert funnel in dip tube inside tank, wear safety glasses and rubber gloves, no splashing. open window. take deep breathe
pour muriatic acid into dip tube and some in bowl, get out of room close door wait 15 minutes,
then flush normally 10 times to dilute any acid in lines.
you will likely see brown scunge running down from bowl rim thats the sediment disolving. this really works.
if not enough water enters the bowl not enough leaves to generate the force to carry solids.
generally watching a afflicted toilet you see water just swirling in a circle, rather than going down fast