When you guys say Mothers' 3 step system, are you referring to their Ultimate Wax system? If you are trying to removing bird etching with that system, by hand, it's not going to happen. Whether by hand or machine you need to use a cutting pad and a compound or swirl remover to level the paint around the etchings. But, you all are right to be careful when using compound on Subie paint, whether by hand or machine. I cut through a clear coat crack on my 05 hood, by hand, using the cutting side on a German applicator and Pinnacle's XMT 4 compound. I would wash the car clay the area with the defect, then use the pre-wax cleaner, and follow that with a swirl remover and a cutting pad. Keep an eye on your work by wiping the area clean of polish/compound and making sure you are not cutting through the clear. Sometimes a true filler glaze is the best way to cover the defect if you are not willing to risk removing too much clear coat paint. Then put a quality paint sealant over it. I recommend you guys use a paint sealant, not just a wax, to mitigate these etchings. Wolfgang Deep Gloss Paint Sealant and Klasse High Gloss Sealant Glaze are two of my favs and very durable. You can top these with your fav carnauba wax to add a layer of protection and shine/gloss. Always remove contaminants like bird droppings and bugs ASAP to prevent etching. Keep a quick detailer, spray-on car wash, or glass cleaner, with a clean, quality microfiber clothe in the vehicle to take care of these contaminants while on the road.
Hope all goes well with these issues.
P.S. And posting pics would help to diagnose a solution as well.