D6 to D7 upgrade fails on a number of tables ("already exists")

I've spent hundreds of hours trying to get an old D6 site upgraded to D7 and I keep encountering errors like the following:

Cannot add index system_list to table system: index already exists.
Cannot rename blocks to block: table block already exists. [error]
Cannot rename comments to comment: table comment already exists. [error]
Cannot rename filter_formats to filter_format: table filter_format already exists. [error]
Cannot rename filters to d6_upgrade_filter: table d6_upgrade_filter already exists
Cannot rename filters to d6_upgrade_filter: table filters doesn't exist
Cannot rename profile_fields to profile_field: table profile_field already exists. [error]
Cannot rename term_data to taxonomy_term_data: table taxonomy_term_data already exists. [error]
Duplicate entry 'modules/update/tests/aaa_update_test.module' for key 'PRIMARY': INSERT INTO {system} 
Failed: PDOException: SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry 'garland-system-help' for key 'tmd': INSERT INTO {block} (module, delta, theme, status, weight, region, pages, cache) VALUES
Failed: PDOException: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'drupal.field_config_instance' doesn't exist: INSERT INTO {field_config_instance}
Fatal error: Call to undefined function field_read_fields() in /var/www/www.example.com/modules/field/modules/field_sql_storage/field_sql_storage.install on line 16
Integrity constraint violation: 1062 Duplicate entry 'modules/update/tests/aaa_update_test.module' for key 'PRIMARY': INSERT INTO {system}
Table blocked_ips already exists. [error]
Table date_format_type already exists.
Table field_config_instance already exists
Table filter already exists
Table forum_index already exists.
Table role_permission already exists

I realize this is probably several problems rolled into a single request but I am at my wit's end here. Somebody please help me.