Firstly, I really appreciate how much you know about your own way of operating in the world around you. I would say that, in general, you are spot on in both of your observations: mindfulness can work to manage high neuroticism and mindfulness can often be difficult for someone to implement when they are low in conscientiousness. However, I would like to offer a few alternatives to the way you are framing it and to see if we can support some additional changes for you!
Firstly, I want to support that both personality components - being high in neuroticism and being low in conscientiousness - bring both strengths and areas for growth. Sometimes, the best way to start making change is to focus on what each trait brings to your life and what skills you can use that you already have (and possibly feel negatively about). Starting with being high in neuroticism, high neuroticism is a trait that people have when they are assessing for risk, and are good at assessing risk! This is an awesome skillset to have, especially when we can work to build in some parameters around when you use it and when you are able to turn it off or better manage it (decreasing its impact on it is not necessary). So, on the surface, being able to build in parameters sounds like something that will not work when you are low in conscientiousness (since folks low in conscientiousness tend to be more unstructured in general). However, I think that is an oversimplified interpretation of the role being low in conscientiousness can play in your life and in managing neurotic traits. In fact, people who are low in conscientiousness have the capacity to be more flexible than the average person, and while this might mean that consistency in mindful practice can be a bit harder to maintain, it also means that your ability to find alternative ways to engage in mindful practices is much more likely than for someone who is higher in conscientiousness. Being low in conscientiousness does mean that ups and down are more common for most folks, but it also means that as you try to manage the ups and downs, you can use that flexibility in emotion and in thought to help yourself to manage these different experiences, if that makes sense. This would be something a therapist could help you build some simply structure with so that you can apply it without any strict structures that make it difficult to continue.
One of the simplest ways to use these two parts of who you are together is to focus a bit less on the high in neuroticism piece and instead work on boosting youur conscientiousness. Many people practice this by focusing on adding a schedule in to your daily life wherever you can. It is important to note that this is where some of that flexibility comes in to play to get you started a bit more successfully. It does not matter what the schedule is or looks like. There is not a right or wrong wayy to set a schedule. Some people start with something simple - eating each meal at the same times each day or scheduling when laundry happens or when groceryy shopping occurs and maintaining that for 3-6 weeks. Other people feel it is more helplful to schedule work days and to not have a schedule on non work days. What is important is that you create a schedule in a way that you can most successfully follow through on it and schedule in some thing that you enjoy or want (essentially, something like a reward) that you give yourself when you have achieved something in the schedule. That is actually one of the reasons that some people do not have schedules on non work days. In that scenario, what they get for having followed the schedule all week is time to just not have to think about it again. That does not work for everyone, but for some people, it is great motivation.
I also want to mention that one of the most important things you can offer yourself is the belief that you can make changes whether or not you are able to stay consistent or whether or not you have some struggles or lapses over time. While moments now feel like major evidence of failure when we struggle to do something or we struggle to change behaviors, in truth it is more likely that you will return to that skilll buillding over time, try again, and get a little better at it (for example, a little more conscientious) over time. It is a life long journey to try and find our best selves and it is necessary to give our selves the benefit of the doubt in this process. It is negative self talk and negative beliefs that set up a situation where you feel that your personality traits are things to be fixed or changed, and I want to challenge you to give yourself some additional thoughts of appreciation that you are able to assess risk so well and that you have the flexibility that comes with low conscientiousness to bring into your life and into the ways you see yourself. You bring a lot more skills to your own life and to the life you want to have and the person you are striving to be. By accepting these pieces of who you are, you open up room for growth and for self love that can reduce the lows you experience and increase the possibilities for maintaining some kind of consistent (if varied and flexible) mindful practices over time.
Focusing on what you bring to your life, and knowing that there are benefits to all personality traits can help you to also remind yourself (and hopefully over time start to believe) that you are doing ok, you are going to be ok, and even when it does not feel ok, it is more likely than not that things will work out. It is those internal thoughts and beliefs that can get us down and bring us low, and you have the ability to adapt those, even if it through small steps like telling yourself "I am ok".
I hope this helps. Take care, and keep growing! You are doing great!