I know social media can be convincing and make you think there is an easy way to address this, but orthodontics for this sort of cross-bite is the most ethical way to go. If you do go the veneer route first, you will run the risk of them popping off frequently. Be prepared to pay a lot of money for taking the short-cut. Braces first, and then veneers after braces if you still want an enhanced cosmetic appearance.
If your veneer is AT LEAST standard quality ceramic, the material is designed to mimic the physical properties of enamel. There are no unique or special methods for cleaning a veneer differently than other teeth. Rest assured, as long as you are not switching dental offices every 6 months, your dental hygiene professional will be aware and do the cleaning without inflicting any harm to the veneer. No need to tell them "don't damage my veneer" at the beginning of every cleaning, either :)
Thanks for your post! Maybe I can shed some light on what I see here. Dental cosmetics relies heavily on proper proportions and ratios. What you are noticing is not that the teeth are too "big", but rather, the central incisors are equally wide as they are tall, leading to a square shaped veneers that may come off short and bulky. So what is the solution? Ideally, a facially-driven "digital smile design" is best for your type of situation. Using photos and high resolution digital impressions, a dentist and lab would work together to plan out the correct proportions that are aligned with your facial features. In order for this to work, you would absolutely need to have some sort of gum recontouring, typically with laser, in order to allow more space to add to the veneer height. This would also decrease the slightly excessive gum showing. Without adding height to the veneers in the direction of the gums, it is pretty much impossible to achieve the look you are desiring.
In general, what you describe suggests that you may not have had a thorough comprehensive exam before getting your composite veneers. Bad taste and smell can come from a variety of untreated issues, including but not limited to cavities, moderate to severe gum disease, dental abscess, and more. When left untreated, cavities tend to grow deeper over time - this is why you may not have noticed a bad taste until now. While many patients desire cosmetic care, it is crucial to rule out these conditions before any cosmetic work is done. Even with the best at-home hygiene care, existing dental conditions cannot be cured once they exist (regardless of what influencers on social media will have you think). I highly recommend you get a full exam with complete set of xrays and consider any recommendations to treat the findings of that exam.