SELECTING multiple copies of some rows, single copies of others for INSERT

You are on the right track but you will need to join to a table containing the id values:

INSERT INTO owned_instances (template_id, owner, property1, property2, etc)
SELECT
    i.id,
    '478aa65e-ecf7-48fb-bc20-f7fcf300aaa9',
    t.property1,
    t.property2,
    t.etc
FROM templates t
INNER JOIN (
    SELECT 1 AS id UNION ALL SELECT 1 UNION ALL SELECT 1 UNION ALL
    SELECT 2 UNION ALL SELECT 3
) i
    ON i.id = t.id;