I also share the same curiosity with Dana, in that your vet mentioned two things I would not typically expect. One is that neutering males should wait until 5-6 months, and second is that neutering will not improve the behaviors you mentioned.
For the former, perhaps it’s something on the vet’s end where he/she/they are not personally comfortable with operating on a rabbit who’s that young, but from my experience and what I’ve discussed with others, many male rabbits are neutered much earlier. It is less risky than a spay, which is more invasive, and some parts of a spay may be incomplete because the rabbit is not fully developed yet. With males, as soon as the testes descend, they are good to go generally, haha.
For the latter, I read many of those behaviors as being hormonal. A neuter may not be a miracle finger snap, but understanding that many of those behavioral instances are driven by the hormonal urge to mark, defend, and mate makes it unusual to believe a neuter would not improve them. The week approaching my Wick’s neuter, he’d spray me constantly (something he hadn’t done until his testes dropped). The day after the neuter, he sprayed me once, and then never again.
First and foremost, I think having a gut-instinct of whether a vet seems capable is important. Especially when starting off with your first rabbit, I think it is also important to look online and see if what your vet advises and recommends matches your own research! Some vets have really great intentions and believe they are doing their best, but sometimes intentions don’t match practice.
To address the meat of your question, it can somewhat be a losing battle to train some of those behaviors out of an unfixed male. Increasing accessibility to litterboxes, recognizing when it’s going to happen and pre-empting it, cleaning up immediately afterwards.. .these are definitely the primary forces people use to help deter inadherent peeing and pooping. In terms of engraining bad behaviors, to an extent it’s insightful and good to have those concerns, but also neutering tends to be a new starting point for an owner and their rabbit — it’s a time to begin developing a solid relationship that isn’t mediated/moderated by the rabbit’s hormones! Your rabbit is still young and there is plenty of time to develop great habits and a good relationship.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.