Change required in org.activiti.rest.api.history.HistoricTaskInstanceBaseResource.allowedSortProperties.
The keys of the allowedProperties entries do not match what is JSON keys of the result returned by the query. For example startTime is the field returned in the result, but sort key is "start", but for endTime the key is "endTime".
id, parentTaskId, claimTime should also be included in allowedProperties.
These inconsistencies raise API usability issues and there is no other way but to walk through code to identify the problem.
Just from coding standard point of view, keys in allowedProperties and relevant org.activiti.engine.impl.HistoricTaskInstanceQueryProperty statics field names can be the same.