Modelling and querying multiple related fact tables

Good day!

Apologies if this is the wrong place to ask this sort of question.

I have a relational data source with 3 fact tables which are related to each other and model

patient doctor visits (EncounterEventFact table), assignment of a diagnosis to patient (DiagnosisEventFact table) and collecting lab results for the patient (LabComponentResultFact table) in the picture below. They all share EncounterKey a key, specifying a unique visit to a doctor. All EncounterKeys are in EncounterEventFact table and only once. I am using SSAS tabular in memory to model the data.

Each fact table has a few million rows (2-4 mil). DiagnosisDim has few tens of thousands of rows. PatientDim has few millions rows (<10 mil). LabDim has few hundred records. This is a simplified model with just 3 main dimensions.

My measures are a distinct count of EncounterKeys on DiagnosisEventFact and distinct count of EncounterKeys on LabComponentResultFact.

The sample report which is being developed is given a selection on diagnosis dim side, show counts of unique visits for this diagnosis and counts of lab collection visits for this diagnosis. 

diagnosis           count_visits_diagnosis                count_visits_labs

-----------------------------------------------------------------------------

ABC                         5                                          0

DEF                         10                                        5

etc

The problem comes when I select ALL diagnoses in the report. Counts for diagnoses measure loads instantly, while counts of labs measure takes forever. When I select a few diagnoses report works fast.

How to improve my SSAS tabular model or computation to handle this sort of reporting efficiently? 

Unfortunately I can not re-model data on the data source side.