I would just let it be a mess. Maybe change cage papers, but do it fast, don't make eye contact and just get out of the room quickly. Same for feeding. Just do it. Don't mess around. Swap bowls a couple times a day, dump in the new food and leave. Don't look, don't talk, don't touch anything else. Unless you already have experience with raising day one babies, I'd give the pair a shot at getting it right. If they never get the experience of raising their own babies, you can easily end up with a very productive pair that you always have to incubate and raise babies from day one. Follow the same procedure as above for checking the eggs. When in doubt, just don't do it. Around the time you think they should hatch, pick a time when the parents are already off the nest and take a quick peak. I mean quick. 5 seconds. Less would be better. Only check every few days. Less would be better. Don't talk, don't make eye contact. Give the parents a few super prized treats that take time some time to eat while you are checking. In shell almonds work for mine. The large, sometimes nasty smelling poops are normal for a properly incubating female. She holds it while sitting on the eggs and only goes a few times a day. As you start to approach an approximate hatch date, rather than bothering the parents to confirm that an egg has hatched, just assume it has and make sure to give plenty of a wide variety of soft food a few times a day. Do not obsessively check the nest around hatching time. When in doubt, just don't do the thing(cleaning, checking, talking, changing toys etc)...less is better. If you think things are gross, you have clearly never been around a natural nest with older babies. If you can't smell it when you walk in the room, and it's not attracting bugs, and the babies aren't actually sitting in wet filth all the time, it's probably okay. Once they get to hand-feeding age, I will use the level of nasty in the nest box to tell me when I need to pull for hand-feeding. Some species will let you do a partial bedding change and not have a problem. Amazons will have a problem.
If the eggs hatch and parents prove that they are terrible parents and babies die or become injured, then it's time to change things for the next round. Only then would I think about getting a good incubator and hatching and raising from day one. Honestly, if that happens, I'd seriously consider just retiring the pair and not letting them breed.
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