Now to the point some have made about the E string. I understand the added benefit of using the E string. And when miced I have took advantage of the low g. But I dont understand how by not using it I might as well be playing guitar. Lol if a basses whole purpose is defined by an E string why do we have any of the other strings?
You have heard some "why not just play guitar?" and a lot of people feel that way for higher tunings on double bass and especially electric. Historically bass instruments have been all over the map when it comes to tunings.
That history is conveniently forgotten by the "EADG is the ONLY way" camp. Not that long ago, basses were three stringed instruments either tuned in fifths GDA or fourths ADG, and sometimes a combination GDG. That low E or C or B string wasn't really possible because of the string technology of the time. That's enough history to establish the point I was trying to make:
The E string doesn't define the double bass.
However, the bass has a very defined role and
should play "bass". In my experience, (especially in the type of music you are playing)
the majority of that bass playing happens inside the octave between the low G and the open G string, occasionally using the notes above or below depending on the key of the tune. If you want to push it, you might use your lowest notes (whatever they are on your bass) or go up to the D on the G string. Even in classical orchestra music, the bass rarely spends any amount of time above that D, and rarely uses the low notes below an E.
Above that D you are not only entering into the range of a guitar, but also exiting the range bass is usually played in. That part of the bass is usually used for fills, solos, and other "hey everyone, look at the bass player!" moments. While sparingly those can be great moments, it is very easy to over do it. Critically listening to my own playing when playing folk, singer songwriter, jazz/blues, in my Afro-Latin Polka project or any other "acoustic" bass styles,
I use the higher notes less and less. I find that instead of adding something innovative, even the most thought out ideas easily sound like "noodling" or "hey everyone, look at the bass player!" moments.
There are obvious exceptions to this. Edgar Meyer uses the whole bass, and occasionally some high notes I didn't even know were on the bass. While it's difficult to apply a genre to his music, it does flirt with the ones you mentioned. It is completely possible to use higher notes without drawing unnecessary attention to yourself.
As much as I would enjoy having a high C string (or the E above that in 5ths) it wouldn't be something I would use very often under "normal" circumstances. I think you will find that it's mostly a place holder, and you will use the other three strings far more. I would keep the low E string (even if you don't use it very often) because I don't see the high C getting much more mileage.
Sorry for the length. Ultimately it's your decision and it sounds like your bass could benefit from a luthier making some adjustments to maximize the potential of your E string. I think that would be a better way to spend your money than a high C string.