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UPDATE:

I ended up making things significantly more efficient by moving the PIVOT operation into the SQL query itself; that way, SQL Server only has to output the number of rows in the Record table rather than that multiplied by the number of organizations (not too bad until you get to hundreds of organizations, at which point it's a huge number). The operation still takes a few minutes, but it's much more bearable. Here's the query I finally decided to use:

SELECT *
FROM (
    SELECT
        rec.[Id]                         AS RecordId,
        'Org_' + usr.[OrganizationName]  AS OrganizationNamePrefixed,
        COUNT(hist.[Id])                 AS TimesDownloaded  -- To be aggregated by PIVOT
    FROM (
        SELECT
            innerRec.[Id]
        FROM
            [dbo].[Record] innerRec
        INNER JOIN
            [dbo].[RecordClassificationLink] innerLnk ON innerLnk.[RecordId] = innerRec.[Id]
        -- WHERE (classification ID is foo or bar), for optional classification filtering
        GROUP BY
            innerRec.[Id]
        -- HAVING COUNT(innerLnk.ClassificationId) = (number of specified classifications), for optional classification filtering
    ) rec
    CROSS JOIN [dbo].[AdamUser] usr
    LEFT JOIN (
        SELECT * FROM [dbo].[MaintenanceJobHistory] WHERE [CreatedOn] > 'eg. 2016-01-01 12:00:00' AND [CreatedOn] < 'eg. 2016-12-01 12:00:00'
    ) hist ON hist.[AccessingUser] = usr.[Name] AND hist.[RecordId] = rec.[Id]
    GROUP BY
        rec.[Id], usr.[OrganizationName]
) srcTable
PIVOT  -- Pivot around columns outside aggregation fn, eg. heading column [OrganizationNamePrefixed] & all other columns: [RecordId]
(
    MIN(srcTable.[TimesDownloaded]) FOR [OrganizationNamePrefixed] IN (...list of ~200 columns dynamically generated...)
) pivotTable
INNER JOIN [dbo].[Record] outerRec ON outerRec.[Id] = pivotTable.[RecordId]

I added various indexes and also made the PIVOT as efficient as possible by only selecting the aggregation column, the headings column, and the necessary other column(s) to pivot around. Lastly, I re-JOIN the Record table using the RecordId PK to get the extra record info per row.

Typical output:

However this output gets turned into an Excel spreadsheet along the lines of the following by the calling program (hence its being like a PIVOT operation):

.----------------------------------------------------------------------.
| Filename | Creation Date | #times downloaded by: CompanyA | CompanyB | ...
| foo.png  | 1/2/3         |                       0        | 2        |
| bar.png  | 1/3/4         |                       3        | 1        |
...

CREATE TABLE [dbo].[AdamUser](
    [Id] [uniqueidentifier] NOT NULL,
    [Name] [nvarchar](200) NOT NULL,
    [UserGroupName] [nvarchar](50) NOT NULL,
    [OrganizationName] [nvarchar](50) NOT NULL,
PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]

GO

CREATE UNIQUE NONCLUSTERED INDEX [UIX_AdamUser_Name] ON [dbo].[AdamUser]
(
    [Name] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON)
GO

CREATE TABLE [dbo].[MaintenanceJobHistory](
    [Id] [uniqueidentifier] NOT NULL,
    [Data] [xml] NOT NULL,
    [CreatedOn] [datetime] NOT NULL,
    [Type] [nvarchar](512) NOT NULL,
    [RecordId] [uniqueidentifier] NOT NULL,
    [AccessingUser] [nvarchar](200) NOT NULL,
 CONSTRAINT [PK_MaintenanceJobHistory] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]

GO

CREATE NONCLUSTERED INDEX [IX_CreatedOn] ON [dbo].[MaintenanceJobHistory]
(
    [CreatedOn] ASC
)
INCLUDE (     [Id],
    [RecordId],
    [AccessingUser]) WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON)
GO

CREATE TABLE [dbo].[Record](
    [Id] [uniqueidentifier] NOT NULL,
    [CreationDate] [datetime] NOT NULL,
    [LastModified] [datetime] NOT NULL,
    [AssetType] [nvarchar](max) NULL,
    [MasterFilename] [nvarchar](max) NULL,
    [GameName] [nvarchar](max) NULL,
 CONSTRAINT [PK_Record] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]

GO

CREATE TABLE [dbo].[RecordClassificationLink](
    [Id] [uniqueidentifier] NOT NULL,
    [RecordId] [uniqueidentifier] NOT NULL,
    [ClassificationId] [uniqueidentifier] NOT NULL,
 CONSTRAINT [PK_RecordClassificationLink] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]

GO

CREATE TABLE [dbo].[AdamUser](
    [Id] [uniqueidentifier] NOT NULL,
    [Name] [nvarchar](200) NOT NULL,
    [UserGroupName] [nvarchar](50) NOT NULL,
    [OrganizationName] [nvarchar](50) NOT NULL,
PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]

GO

CREATE UNIQUE NONCLUSTERED INDEX [UIX_AdamUser_Name] ON [dbo].[AdamUser]
(
    [Name] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON)
GO

CREATE TABLE [dbo].[MaintenanceJobHistory](
    [Id] [uniqueidentifier] NOT NULL,
    [Data] [xml] NOT NULL,
    [CreatedOn] [datetime] NOT NULL,
    [Type] [nvarchar](512) NOT NULL,
    [RecordId] [uniqueidentifier] NOT NULL,
    [AccessingUser] [nvarchar](200) NOT NULL,
 CONSTRAINT [PK_MaintenanceJobHistory] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]

GO

CREATE NONCLUSTERED INDEX [IX_MaintenanceJobHistory_CreatedOn] ON [dbo].[MaintenanceJobHistory]
(
    [CreatedOn] ASC
)
INCLUDE (     [Id],
    [RecordId],
    [AccessingUser]) WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON)
GO

CREATE TABLE [dbo].[Record](
    [Id] [uniqueidentifier] NOT NULL,
    [CreationDate] [datetime] NOT NULL,
    [LastModified] [datetime] NOT NULL,
    [AssetType] [nvarchar](max) NULL,
    [MasterFilename] [nvarchar](max) NULL,
    [GameName] [nvarchar](max) NULL,
 CONSTRAINT [PK_Record] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]

GO

CREATE TABLE [dbo].[RecordClassificationLink](
    [Id] [uniqueidentifier] NOT NULL,
    [RecordId] [uniqueidentifier] NOT NULL,
    [ClassificationId] [uniqueidentifier] NOT NULL,
 CONSTRAINT [PK_RecordClassificationLink] PRIMARY KEY CLUSTERED 
(
    [Id] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
) ON [PRIMARY]

GO