PHP / MYSQL查询执行时间优化

I am having a great deal of difficulty with this set of queries. I cannot find a way to speed up the second query at all. I've tried joining the the first query as a subquery on the second one, running through the first query results one by one and the current setup, all of which have proven extremely slow.

I would like to simply add a limit to the second query instead of this hocky stuff but our mysql version is too old to support it. For some reason it is also treating EXPLAINas a syntax error, which is unhelpful.

How can I reduce the execution time of this?

$limitQuery = $pdo->prepare("
            SELECT r.supplier_option_code FROM third_party_raw_stock_price AS r ORDER BY r.id LIMIT 100
        ");
        $limitQuery->execute();
        $limitIds = $limitQuery->fetchAll();
        $limitIds = implode("', '",array_column($limitIds, 'supplier_option_code'));
        $limitQuery = null;
        $linkColumn = 'supplier_code';
        $thirdPartyId = 'FS';


        $migrateQuery = $pdo->prepare("
            UPDATE third_party_raw_stock_price AS r
  JOIN options_new AS o
    ON o.".$linkColumn." = r.supplier_option_code AND r.supplier_prefix = '".$thirdPartyId."'
  JOIN third_party_config AS t
    ON t.code = '".$thirdPartyId.""'
SET o.price = '989.99', o.cost_price_variation = '3.33', o.stock = '7'
WHERE r.supplier_option_code IN ('$limitIds')
        ");
    $migrateQuery->execute([':config' => $thirdPartyId]);