Confused about Form 8824 - Like-Kind Exchanges

Suppose I buy a rental property for $200k. After a few years I sell it for $300k. I would have a capital gain of $100k (ignoring depreciation, improvements, and closing costs). Rather than pay taxes on the $100k gain, I decide to do a 1031 exchange; I buy a replacement property for $350k.

I am confused by what is entered on Form 8824.

Here is what I think should be entered on Form 8824 according to the IRS (from examples I have seen).

Line 16 - FMV of property received: $350k

Line 17: Same as Line 16 in this example: $350k

Line 18 - Adjusted basis of property sold: $200k

Line 19 - Realized gain (Line 17 - Line 18): $150k

Line 24 - Deferred gain (= Line 19): $150k

Line 25 - Basis of like-kind property received (= Line 18): $200k

These are different from how I think about these transactions.

 * I would think  the realized gain was 0 (since in order to purchase the new property I added $50k to the $300k received for the old property; I spent money, I didn't realize money).

 * I would think that the deferred gain was $100k, since that is the gain I would have had if I didn't do the exchange.

 * And I would think the basis of the property received was $350k, as that is the basis of my new property.

Can someone please confirm whether the amounts I listed as "should be entered" are correct, and explain why they are not what I would think they should be?

Thank you!