Thank you both very much for the replies and kind words, that's really exactly what I was hoping for. Rather than go line-by-line, I'll try to address some of the bigger questions/comments raised.
First off, I absolutely don't think it's callous to suggest thinking about simply keeping him comfortable rather than taking aggressive action. If anything, I'm the one who is feeling cold right now because he's our dog and that is pretty much what my gut is telling me... but I'm trying to remember that, used correctly, euthanasia is a gift. We can't know without checking, but I have a strong suspicion that this is not the only tumor he's got. Even the vet said that while there's no guarantee without a closer look, the protrusion seemed much harder than a primary eye tumor should. Of course, he's not a young dog, which has a big impact on the decision tree. If I were the only one making the decision, I think I'd be leaning on keeping him comfortable and not doing much else. Even though the vet said that the surgery to remove his eye isn't as gruesome as it might seem or sound, I know Bailey and it still sounds like he would be so miserable during the recovery and there's no way it's buying him another ten years.
Not to bring politics into what is a decisively nonpolitical conversation, but frankly I am a big proponent of Physician Aid in Dying in people who are sick, so certainly I don't feel squeamish about the idea or even necessarily making that call when the time comes. Well, just the completely understandable pain at the thought of losing a family member, but not the act or process or correctness of the decision itself. I'm stating the obvious, but it's just a question of when the right time is. I know I'm repeating myself, but with his quality of life where it is now, it seems equally cruel to make the call too soon but I also know it is no better for anyone waiting too long. I completely agree that death isn't so awful, especially when the alternative is living with a terrible, terminal illness. It's hard when he seems so happy and basically OK that we certainly don't feel like we'd be putting him out of his misery, yet, but of course our goal is to save him the misery to begin with.
Before I go on, I do want to mention that my dad spoke with another vet. The eye vet is pretty far away and the trip is hard on Bailey, so they're reluctant to even have to take him down there for tests, let alone potentially a surgery. The vet we spoke to yesterday is much closer. I could be misunderstanding, but it sounds like they're going to take him in on Friday just to get another opinion about what to do (we're not doubting he has cancer or anything). Either on Friday itself or another appointment, it sounds like the nearby vet was suggesting doing an ultrasound first to check his abdomen. This should cost less than the full workup and could still give us information. He has a very suspicious lump on his abdomen and if it turns out that's a tumor, the way forward will be much clearer. He just has a lot of lumps and bumps because of his weight. They could all be fat pockets, or he could be riddled with tumors. We don't know, but I think we are all comfortable that an ultrasound is not too invasive and has the potential to give us information that may make our course more clear.
We actually had the exact same discussion about how the vet from yesterday is nice enough but of course he'd like to be paid 2.5k for removing Bailey's eye. The vet nearby is a little more realistic about what makes sense IMO and is better about trying to find creative solutions to save money (like the ultrasound instead of full x-rays).
I 100% hear you on the advice that it's better a bit too early than too late. I am REALLY hoping we can find a vet to do a house call for it, but I know it's no guarantee. Thank goodness Bailey doesn't mind the vet so if we have to go while he's still mobile, he shouldn't be inherently terrified, but of course you are right that we don't want to have to carry him in when he's already half gone.
I was going to hit a couple of more points individually but I think I can kind of sum it all up here. As much as possible, it sounds like at least the three of us are on the same page (knowing that you two don't know Bailey and can only go from what you've experienced and what I've told you). As of right now, I am really pushing against doing the surgery for a lot of reasons that I've talked about, are obvious, or one of you has brought up. I don't think there's any harm in the ultrasound and it is significantly less expensive. If it turns out he does have a tumor or tumors in his abdomen, then it will absolutely be a matter of keeping him comfortable until the time comes. I mean, even if he doesn't, we may go that route regardless, but this is the first time my mom and I have had to deal with this so it's just hard and she will be the hardest to convince. She doesn't want him to suffer either, though, he is just closest with her and she will take it the hardest. My dad had a dog when he was younger but she died when he was at college, so I guess this is new for us all.
I read last night that for families who have put down multiple pets, they tend to do it sooner and sooner as they've had to do it more. Not cruelly soon, just that it tends to be those having to make the decision for the first time who hold on longer than is good for the pet. I'm trying to keep that in mind. It's so easy to tell yourself that you're making the right decision prolonging things when often, you're not. But we will continue to watch his quality of life regardless and try our hardest to not allow him to get to such a bad spot before we send him off. Truly, he still has a long way down to go, even if it could happen quickly... but at least it's comforting right this second to know he's OK. And it is very comforting to be reminded that he is not thinking about this like us, so thank you.
I will definitely provide updates when we have them.
Edit: Just forgot to address that I completely agree about a "sign" that it's time, or rather the lack thereof, that it is unwise to wait for a single big cue. We are doing our best to continue looking at Bailey's quality of life comprehensively and not waiting until any one or multiple of his faculties begin to truly fail. He still eats 99% of his food, still enjoys treats and occasional human food, still goes on and enjoys [short] walks, no incontinence yet, etc. Really there's nothing major (at this point) I can think of that I would say is significantly impacting his quality of life besides the fact that it's very difficult for him to get up the stairs now and he loves to sleep in my parents' room, but he still manages with help. Anyway, my point in editing was just to say that I will definitely keep in mind that we should not wait for one sign but rather keep track of how well his life is on the whole, one day at a time. Of course, I don't get to see him daily now, but Dad is very realistic about this kind of stuff and I believe will be able to honestly appraise how Bailey is doing, and even Mom is so far handling this better than I expected... but I think that was my fault for not giving her more credit. She's a pretty amazing woman and while I can't stress enough what a wonderful fit Bailey was for our family at that time and how much we all love him, she is the one who will truly be losing her soul mate dog. I'm just worried about her, too.