I disagree.
I am not advocating using olive oil or a 1% Dawn soap dilution in normal cases. According to the OP, this is an extreme case; consequently, this buildup may be fusing to the skin. The most urgent priority is IMO removing the buildup. The second most urgent priority is protecting the exposed skin to avoid it from becoming a chronic wound. The longer this buildup stays on skin, the worse things are going to get. If I did not believe this method would be successful in safely removing the buildup while minimizing additional skin irritation or stress, I would not have recommended it.
Oh please do not oil up your rabbit.
Why use oil to help remove severe dried buildup?
Oil can soften this type of severe buildup and can reduce the amount of scrubbing as well as the quantity of solvent needed to remove the buildup. In this specific case, IMO the benefits greatly outweigh the risks.
Ammonia burns skin and buildup can begin to fuse to the skin. The process of butt bathing a rabbit can further irritate this because the natural body oils are being removed. This can trigger an inflammatory response. The antioxidants and vitamins in olive oil are beneficial to skin health, and it does not clog pores. It can supplement some of the natural skin oils that can be lost from bathing, and protect skin from further damage.
You dont want to add anything to the rabbits skin that will soften it and make it easier to damage.
Actually, that is exactly what I would want in this instance. The oil softens the buildup better than water alone can, and helps gently separate it away from the skin, helping to avoid unintentionally ripping out fur or ripping off skin that is stuck or fused to this gunk.
Nothing should be put on skin unless their are physical wounds. Bunny skin is easy to damage.
Why use a topical designed to reduce and prevent further irritation?
I agree that rabbit skin is very sensitive and easily damaged, hence the need to prevent exposed skin from going from bad to worse.
In this case, the exposed skin is presumably very vulnerable. It is in an area that will make contact with surfaces, have contact with waste products (including ammonia), and is vulnerable to friction burns. The loss of natural skin oils can make this worse. We have products designed to help protect extremely sensitive skin from damage and replenish healthy skin oils (for example, CeraVe.)
With no hair to protect it, why leave such sensitive skin vulnerable to these elements?
Using other shampoos is also not a good idea. Stick with what is safe. It is generally regarded to use nothing but a warm damp cloth unless cases are severe.
Getting the buildup off ASAP is of the greatest importance. A damp cloth is inadequate in this specific circumstance.