Presenting Barely Complete Results
This question is rather difficult to answer without more information, and I believe one needs to have more details to actually judge things. I will do my best to address several of your concerns:

You are right that "a faster implementation of an algorithm" is not something very remarkable by itself. There are two possible interpretations:


Your algorithm does the same thing as the previous algorithm, but you have either changed the insides of the algorithm or performed a better analysis and you have got a better time bound on the algorithm. In this case, I believe it should be okay to publish in an undergraduate journal.
The algorithm is still the same, but you have discovered a flaw in some implementation of the algorithm and corrected this flaw, so the running time actually corresponds to what the original time complexity bound promises. This is more literally "a faster implementation of an algorithm", and by itself is not a large contribution.


The usual methodology in Computer Science for measuring complexity of algorithms is either worst-case complexity, average-case complexity or amortized complexity. You seem to suggest that you have some novel kind of methodology. If that methodology is more useful for some practical problem which you set out to solve, I believe this might be definitely something to include in the publication.

It is difficult for me to estimate the amount of novel work that you actually have, but you seem to suggest that it was a requirement to submit to an undergraduate journal. Therefore, it makes sense to me that you should write up your work regardless and try to submit it.

It is not the end of the world if a grant fails, but you should try and fulfill the requirements regardless. If you do submit, it may happen that your work does not get accepted, but if you fail to submit, this becomes a certainty.