What is the appropriate SQL statement/s to produce a stacked bar chart for multiple random variable distributions?

Question

The Objective

Graph the difference between the probability distributions of sets of random variables that come from a number of different sources using a stacked bar chart (or another type of graph suited for such visualization).

The Problem

I'm not sure of the right combination of SQL SELECT statement(s)/condition(s) to present the data to the graphing tool in the right way to achieve the objective above.

The Method

Summary

Feed the source data stored in Google Cloud Platform (GCP)'s BigQuery into Google Data Studio and use a stacked bar graph to visualize the numerous probability distributions.

The Source Data

I'm dealing with simple binary outcomes, either a heads or tails. One trial (== one second) per source yields between 0 to 200 how many heads (1s) were counted.

The schema of the data we have stored in BigQuery is as follows:

time      | source1 | source 2 | ... sourceN
---------------------------------------------
09:00:00  | 99      | 110      | 95         |
09:00:01  | 101     | 115      | 107        |
09:00:02  | 99      | 91       | 97         |

For a Single Source

The following works fine if I'm trying to graph the results from just a single source. And as the law of probability would say, the graphed distribution is moreorless in fit with the expected bell curve.

SELECT
  source1 AS src1,
  COUNT(source1) AS count
FROM
  `rnddata`
WHERE
  recorded_at >= "2021-03-11 08:45:00"
AND
  recorded_at < "2021-03-11 09:45:00"
GROUP BY src1
ORDER BY src1

src1 | count
75   | 1
77   | 2
80   | 2
81   | 5
82   | 6
83   | 20
84   | 10
85   | 14
86   | 31
87   | 33
88   | 48
89   | 74
90   | 74
91   | 89
92   | 107
93   | 133
94   | 135
95   | 168
96   | 160
97   | 192
98   | 190
99   | 195
100  | 189
101  | 197
102  | 191
103  | 188
104  | 180
105  | 201
106  | 130
107  | 128
108  | 107
109  | 96
110  | 64
111  | 65
112  | 45
113  | 40
114  | 19
115  | 22
116  | 18
117  | 9
118  | 8
119  | 6
120  | 3
121  | 4
125  | 1

For Multiple Sources

I'm thinking that if I can have multiple dimensions (src1, src2... srcN) with a single count column for the metric, then I will be able to graph the dimensions as stacked bars on the X axis and have the count metric set to the X axis.

I imagine the output could be something like this:

src1 | src2 | count
75   | null | 1
77   | 77   | 2
80   | 00   | 2
null | 80   | 5
82   | 82   | 6
83   | null | 20
83   | 11   | null
84   | 84   | 10

I did a bit of research and experimenting with UNIONS and JOINS and INTERSECTS but couldn't quiet get the above output. Any advice on how to form such an SQL statement to do that, or offer a better presentation (schema) of the data for the graphing purposes, would be greatly appreciated.