I have all the same problem like you have and recently gave some hard thought about it. I'm not sure if this will work for you and also maybe someone already suggested something similar (I'm too lazy to read all the comments during work hours :-)) so just a quick note.
Like you, I am anxious about "this next big thing idea" from a few days to a month, then I drop it, and go to "next big idea I have". But what I noticed is that after a couple of months I usually drop something forever (just understood I don't want to do it) OR... and this is interesting - I get back to one of the ideas that I still believe in and work on it again for a while.
Because of that, I always thought that I am somekind of a quitter, but after thinking more about it, and I would like to call this process not 'quitting', but instead a rotation
. I get bored by one, I jump to other, to other, to other, until I jump back to the first one again.
So, I decided to "exploit myself" like this: let's say I have this timeframe of couple of days, before my enthusiasm runs out and I jump to my next project - I have two rules:
1. Always note stuff I need to do or think about later;
2. During that time do small tasks (either new or those noted down last time), that have some visible result.
This way, I am working on all my projects for the amount of time that pleases me, I get something done and I don't call my self 'quitter' or 'not finisher' - I know that I'll get back to/finish them later or drop them for sure.
Of course as this is new idea I've came up with, I have no real results to show off right now, but so far so good - I'm constantly getting back to all of my ideas and doing something significant, step by step.
I hope this helps!