One possibility could be to make the processing a project in itself--your first and, for a while, only, GTD-managed project.
So you could:
- Make your capture list, as you have done.
- Make one current project: "Get my GTD system past initial capture." Or if you do the outcome-description thing, "GTD system past initial capture."
- Create a weekly repeating Action: "Brainstorm capture list for twenty minutes."
- Create a daily repeating Action: "Process ten items from capture list."
- Create a weekly repeating Action: "Compare length of capture list to last week's length."
Now that you have one project, you can work the system. Work those actions. Do your weekly review. Work the system.
The processing will result in new projects. By default, make ALL of those projects Someday/Maybe--don't focus on working them yet.
If the weekly check says that the capture list is growing, increase the ten daily items-to-process to something that might cause it to shrink. Eventually the capture list may shrink to some reasonable size so that you can move the processing to your weekly review. Or it may not; you may make daily processing part of your system.
Of course, at some point, either before or after you reach that steady-state, you have to take some more projects off of Someday/Maybe and actually work them. Since you're already experiencing what I'd call "list overwhelm", set yourself a maximum allowable number of active projects--even if you think that you should be working sixty, only allow yourself to make, say, five of them active. If that works, bump it up to seven. And so on. But if list overwhelm hits, throw some of them back into Someday/Maybe.
You may end up being one of those people that likes to work a couple of hundred projects at once, once you have them structured. Or you may be like me, and dislike having more than five or ten. If you feel like you "should" be able to work hundreds and feel bad that that doesn't work for you, go read about Kanban and minimizing WIP, and feel better.