Yes, you can use the "session" reporting. So if it was all at one game, one location, and one day, you will report a net of $2000, which will show up on Line 21 of Schedule 1.
However, the IRS computer will expect to see $20,000. So you will enter $20,000, but counter-act that by a negative $18,000, so the final result on Line 21 will be $2000. Somebody else can help you figure out how to do that in TurboTax.
As a side note, you mentioned the $1200 threshold for issuing a W-2G. You need to keep in mind that you need to report ALL session-wins, not only ones that show up on a W-2G. The session-losses will be an Itemized Deduction on Schedule A, as Critter mentioned below.
