Why are they fighting? Why is your router aggressively reusing the IPs as soon as the lease expires?
In my house, all of my devices end up with pretty stable IPs (even non-Apple ones) and I haven't done anything special to configure this. I assume my router holds onto previously-assigned IPs in case the device comes back as long as there's still unassigned IPs available to give out to new devices, though I haven't investigated it.
Clients will usually request their previous IP in the request, and servers will often prefer to give clients their previous IP even if they don't request it. It's also pretty common that the client still has a valid lease (as far as the server is concerned), which it makes sense for the server to reissue.
In my house, all of my devices end up with pretty stable IPs (even non-Apple ones) and I haven't done anything special to configure this. I assume my router holds onto previously-assigned IPs in case the device comes back as long as there's still unassigned IPs available to give out to new devices, though I haven't investigated it.