I had very similar problem and I was able to find a solution.
Query starting with SELECT * FROM (SELECT SCHEMA_NAME([o].[schema_id]) AS [SchemaName],
from [sys].[spatial_indexes]
and other tables had suboptimal plan and was running for hours, causing VS to timeout and retry.
Plan guide included below solved the problem for me.
Because VS sends all queries in one batch during 1st attempt to get results plan guide will not kick in. After query times out, VS will retry this query in its own batch and plan guide will be applied.
To speed up the process even more and don't wait for time out you can kill VS session when it is stuck on this query and force retry.
EXEC sp_create_plan_guide
@name = N'VS Schema Comp Spatial Idxs',
@stmt = N'SELECT * FROM (
SELECT
SCHEMA_NAME([o].[schema_id]) AS [SchemaName],
[si].[object_id] AS [ColumnSourceId],
[o].[name] AS [ColumnSourceName],
[o].[type] AS [ColumnSourceType],
[ic].[column_id] AS [ColumnId],
[c].[name] AS [ColumnName],
[si].[index_id] AS [IndexId],
[si].[name] AS [IndexName],
[ds].[type] AS [DataspaceType],
[ds].[data_space_id] AS [DataspaceId],
[ds].[name] AS [DataspaceName],
[si].[fill_factor] AS [FillFactor],
[si].[is_padded] AS [IsPadded],
[si].[is_disabled] AS [IsDisabled],
[si].[allow_page_locks] AS [DoAllowPageLocks],
[si].[allow_row_locks] AS [DoAllowRowLocks],
[sit].[cells_per_object] AS [CellsPerObject],
[sit].[bounding_box_xmin] AS [XMin],
[sit].[bounding_box_xmax] AS [XMax],
[sit].[bounding_box_ymin] AS [YMin],
[sit].[bounding_box_ymax] AS [YMax],
[sit].[level_1_grid] AS [Level1Grid],
[sit].[level_2_grid] AS [Level2Grid],
[sit].[level_3_grid] AS [Level3Grid],
[sit].[level_4_grid] AS [Level4Grid],
[sit].[tessellation_scheme] AS [TessellationScheme],
[s].[no_recompute] AS [NoRecomputeStatistics],
[p].[data_compression] AS [DataCompressionId],
CONVERT(bit, CASE WHEN [ti].[data_space_id] = [ds].[data_space_id] THEN 1 ELSE 0 END)
AS [EqualsParentDataSpace]
FROM
[sys].[spatial_indexes] AS [si] WITH (NOLOCK)
INNER JOIN [sys].[objects] AS [o] WITH (NOLOCK) ON [si].[object_id] = [o].[object_id]
INNER JOIN [sys].[spatial_index_tessellations] [sit] WITH (NOLOCK) ON [si].[object_id] = [sit].[object_id] AND [si].[index_id] = [sit].[index_id]
INNER JOIN [sys].[data_spaces] AS [ds] WITH (NOLOCK) ON [ds].[data_space_id] = [si].[data_space_id]
INNER JOIN [sys].[index_columns] AS [ic] WITH (NOLOCK) ON [si].[object_id] = [ic].[object_id] AND [si].[index_id] = [ic].[index_id]
INNER JOIN [sys].[columns] AS [c] WITH (NOLOCK) ON [si].[object_id] = [c].[object_id] AND [ic].[column_id] = [c].[column_id]
INNER JOIN [sys].[objects] AS [o2] WITH (NOLOCK) ON [o2].[parent_object_id] = [si].[object_id]
INNER JOIN [sys].[stats] AS [s] WITH (NOLOCK) ON [o2].[object_id] = [s].[object_id] AND [s].[name] = [si].[name]
INNER JOIN [sys].[partitions] AS [p] WITH (NOLOCK) ON [p].[object_id] = [o2].[object_id] AND [p].[partition_number] = 1
LEFT JOIN [sys].[indexes] AS [ti] WITH (NOLOCK) ON [o].[object_id] = [ti].[object_id]
LEFT JOIN [sys].[tables] AS [t] WITH (NOLOCK) ON [t].[object_id] = [si].[object_id]
WHERE [si].[is_hypothetical] = 0
AND [ti].[index_id] < 2
AND OBJECTPROPERTY([o].[object_id], N''IsSystemTable'') = 0
AND ([t].[is_filetable] = 0 OR [t].[is_filetable] IS NULL)
AND ([o].[is_ms_shipped] = 0 AND NOT EXISTS (SELECT *
FROM [sys].[extended_properties]
WHERE [major_id] = [o].[object_id]
AND [minor_id] = 0
AND [class] = 1
AND [name] = N''microsoft_database_tools_support''
))
) AS [_results];
',
@type = N'SQL',
@module_or_batch = NULL,
@params = NULL,
@hints = N'OPTION (FORCE ORDER)';