TurboTax Online can only handle 500 transactions, while Desktop should handle about 2,000, although downloads with that many transactions sometimes fail. Instead of downloaded individual transactions, you can enter summary totals, as you mentioned. When entering summary totals, there is a workaround when gross proceeds (or cost) exceeds $9,999,999.99. Split the category in to multiple transactions. For example, if your Short Term transactions reported to the IRS (Box A) totals $14,000,000, simply split it in to two summary transactions of $7,000,000 each. It's a little more to enter, but it beats entering 1,400 transactions.
For information on entering Summary Totals, see the following FAQ: