As I mentioned earlier, there are many ways to set this up and make it work as long as you do not have any issues, such as a unhappy customer, someone saying they did not receive, or someone who pays for 90% of the layaway and decided they do not want to follow through and want their money back. I would guess you could write it up any way you liked, but if the whole policy of lay-aways and multiple payments is against Etsy policy, I would bet they will side with the seller every time, and require a full refund to the buyer.
In the case of a partial payment needing to be refunded, it is not a huge deal, after all you still have the merchandise, so you are not really out much, but in the case of payment being made in full, and a customer saying they bought three items and only received one, you will lose the case as you will not have tracking for each individual purchase.
I do not know if Etsy enforces policies and restricts or takes away selling privileges here for not following policy, but I am doing too good here to jeopardize any possibility by doing these things.