How should I approach this unfinished research that I do not want to do? I am about to finish an undergraduate degree, with a good enough GPA that even if I got C's in all of my current classes, my final overall cumulative GPA would remain above 3.6.

Assuming I graduate with all the whistles in my diploma it would be:

Honours Bachelors of science in computer science with distinction and a minor in pure mathematics (quite pompous).

In order to complete all of those whistles I had to do supervised research for two semesters. Being a naive undergraduate, I knocked on proffessor's doors, asking for a supervisor, and one of them, very generously agreed. He suggested a problem I thought was interesting and so I started the research. I originally started throwing analysis at the problem, and started trying to solve some really complex differential equations (which kept me motivated). However I did not make much progress, so after my supervisor marked that I needed to get something, I fully changed my approach and started using some geometric approximations to solve the issue. This generated some results, but was too simple. I'd like to say that my results were inversely proportional to how much effort I was putting in the research.

Time passed, I had multiple potential solutions and a way to evaluate them. On the last week before the final submission I realised there was a bug in my code base that was destroying the results (they were mathematically impossible). I tried to find the error, but the best I could do was identify an area where a mistake could have happened. 

Finally I got my evaluation on the course after presenting it. The feedback said the methods were a bit naive and could be improved on, and it was dissapointing that I didn't get numerical results (I had visual results, not numerical), however since I was not a seasoned researcher they decided to be lenient and gave me an A anyway.

I applied to the grad program at my university, and asked the same proffessor to be my supervisor for the grad program. I am in desperate need of financial support until the grad program starts, and so my supervisor said I could do summer research for him and in the meanwhile we could discuss what the grad project could be. What he wants me to do is finish my previous work and get a publication. 

The issue is that I legitimately feel that dinking bleach would be more motivating (I am using this metaphor to convey just how much anxiety this is giving me). This research really does not appeal to me in any way or form, and the interesting part is over, all that is missing is finding the bug, which could take more than two weeks to solve and implementing a couple of modifications to make my naive methods less naive if things go well, or complete failure to finish it in the worst case.

In addition to that I have been doing independent research simultaneously as I have been taking courses and doing everything else. Although this independent research still needs a lot of work, it's in a good place, I have already improved many of the papers I have read and have multiple ideas to explore. In an ideal world I would win the lottery tomorrow and I could just support myself while I carry on with this research.

I am not sure how to approach my supervisor and tell him I don't want to finish this research, nor how to suggest to do my research instead and get a publication out of that, or even if I should touch on this topic at all.
Talk to your supervisor when you know how long you will need to finish the publication.

You are currently in the phase of a project where you have to make very sure everything really works. This is usually the least motivating stage, but it is absolutely necessary. So your supervisor will (hopefully) push you to go through this phase and finish the publication, because finishing research projects is something you have to learn as a budding researcher.

Of course, not every project should be finished. If the costs (time invested) of a project outweigh the benefits (results and publication strength), your supervisor may want to abandon the project. It is important to find out how long you still need, and only then (if still applicable - maybe it's a two-week bug fix that doesn't feel like drinking bleach) have a discussion with your supervisor. You can bring up your independent research during that discussion as well - either as an alternative or as a next project.