You mention a few factors that make me feel like you are viewing this as more of what I would call an internship than an regular job. The big difference being that an intern accepts being underpaid because they are learning, building a good job history and entered the job with fewer skills - so they are potentially less productive. In these cases, an intern trades time at the job working thankless hours for thankless money for a better resume and good potential future work.
When you mention your relationship with this job, I hear:
I'm not the most productive employee, but I am extremely punctual, polite, and well liked. - this usually advice I give interns - before you have "cred" in your field, make sure you hit the easily measurable metrics of timeliness, good manners, and good attitude.
I wrote "amazing" because the experience I'm gaining is corporate software company experience. - I'm betting that mileage varies a lot here. My first job out of college was amazing for the same reason, but being corporate software, the money was pretty great. But this is going to have a lot to do with where you live, your job history, and your personal situation. If what you feel is that a significant part of your "pay" is the experience of working in the company which will lead to a better career in the long run, then it fits into the internship model.
It's more of a resume builder and the company is well known in my town so it's a good stepping stone to another job. - similar to the previous bullet - if you are getting enough training and good skills at this job that another one will eagerly snatch you up because you've worked at this company, then it might be an unspoken internship.
My point in highlighting this is that interns are generally expected to trade time for knowledge. If you aren't getting knowledge, then your time isn't worth it. If you are, then you are getting paid more than the lousy salary. In most internships, I expect the intern to be around slightly more than the bare minimum, because they are expected to pick up the slack that the more skilled and better paid employees need. I won't know when that will happen, so I want them around. The tradeoff is that they don't need to work quite as hard or as thoughtfully, because they are primarily learning.
"I don't work very hard but I don't I need to be considering I'm the
least paid software engineer in the country"
If you are capable of independent work, don't need that much supervision or have the skills you need to do the job with little help from others - then you don't fit the intern model so easily - you fit the model of an employee who is, quite frankly, slacking. I'm not sure what to say here, other than to put out the thought that regardless of what you are paid - you made the agreement to work for some number of hours in return for some hourly wage. Not being very productive because the wage isn't very good isn't a good excuse. If you want a better wage, find a company that will pay you a better wage.
I point this out because when I interview people, I like to learn what they did. The excuse "not much because my salary was lousy" doesn't hold much water with me. Either you are a go getter who did great things in your last job and will do great things for me (the hiring manager) in your new job, or you are not. And a great company reputation isn't going to change my mind if this what I hear in the process of doing an interview.
Part Time in Corporate Life
I'm a huge advocate of part time work. I love it, and I've seen many teams and individuals benefit from it as it gives a great advantage to work life balance. My best part time people have been people who would be go-getters regardless of the situation, but who found a way to balance life and work better with a reduced number of hours and a reduced salary. The absolute best have also been very sensitive to the work/life tradeoffs so that they were able to be at work when we most needed them - making sure that they had time at work during optimal working hours, and enough slack personal schedules that they could help out when the team was in crisis - just like a full time person would.
The trick is - it isn't really a fix to anything. A great job and a great employee can do just as well together part time as full time. But a not-great job and a not-great employee tend to be a worse combination then they were at full time. I'm sure there are tons of management theories on this, but my experience has been that there are two factors:
it's harder to measure them - it's hard to say in knowledge work what 50% is, so it's harder to give critique when someone is doing badly. When someone is doing really well, it's easy to see that the 75% they did was better than the 50% of the hours they worked, but when someone is contributing 40% and being paid 50% --- well, it just starts to get confusing, especially when there is only one person on the team who is working unique hours.
there is a value to availability - working in an engineering team means having a stake in the shared knowledge and shared decision making - no team can build things with each team member in isolation. When one team member has less availability than the rest of the team, it makes getting together for meetings, or sharing knowledge a bit more difficult as there as a significant percent of the time when said team member is not available. This is a loss of value that's extremely hard to account for in monetary terms.
If you are intent on part time work here, you need to find a way to answer these questions favorably for your boss. Quite honestly, if my least-performing engineer came to me and asked for this kind of special consideration, I'd probably say "no". My goal is to get everyone contributing as much as possible, and if I already have a problem area, I'm not going to make the situation more complicated by making special working arrangements.
But - if you can find a case where your reduced work hours really help the company's best interests, you may have a good case. This may take ingenuity - if the company is strapped for cash, needs a specialized skill set, but only for a few hours a week, etc - then there may be a special need that lets you fill the niche and get what you want. The problem can be, that this niche may result in less marketable skills - which would run counter to your goal of being more marketable and better paid in the long run.