In these sorts of situations a 1031 like-kind exchange might make financial sense, but not logistical sense.
The good news is that the tax code allows what's known as a "reverse exchange," which lets you buy the replacement asset first and sell the relinquished asset later. You can keep using your existing asset in the meantime, and you still get all the benefits of a forward exchange - that is, the ability to defer recognition on the gain from the sale, which can exceed 40% of the proceeds in some cases.
Reverse exchanges aren't as well known as other types of 1031 exchange and we get a lot of questions about how they work. So we've pulled together a more detailed resource that explains what it is, how it works, etc. We encourage you to take five minutes and have a look.