How to flatten a very complex object in Illustrator?

I have this design I’m working on, I reached this point where the main object is like I want but it got really really complex.

Now, I want to keep only visible parts of it (what I see only), and discard everything else. (by flattening shapes layers, and keeping them in one layer of adjacent shapes)

I tried all I know to achieve this but I can’t seem to do it without ruining transparencies, colors and clipping masks.

What I see (what I want to keep):
enter image description here

What it looks like without the white circle in the middle:
enter image description here

How complex it is in outline mode:
enter image description here

Is there a way to achieve this??

EDIT:
As requested, here is the Ai file: https://goo.gl/Us3Vil

Thanks to everyone for the help!

EDIT 2

Thanks your everyone for your help, all of your solutions are helpful in different aspects.

I chose wch1zpink’s answer because my work is Illustrator based and it really enhanced the performance in a noticeable way.

-I hope someone would find a more accurate solution to this problem, and post it, which would help us all in the future if we wanted to achieve the same thing.

Answer

I deleted all my previous solutions after realizing that the easiest solution would actually be.

  1. for convenience purposes, select that topmost circle in the image and go to your layers panel and create a new layer for the circle only and place that circle in the new layer.
  2. toggle the visibility off on that circle layer so all you see is the art work with all the gradients. Copy that circle artwork to your clipboard

enter image description here

  1. size the artboard to “fit to artwork bounds”

enter image description here

  1. save and close that document
  2. create a new illustrator document
  3. go to menu item File/Place then select your original file you just closed and saved. Be sure to check the “Link” option.

Now your original gradient vector is placed as one solid object in your new file.

  1. paste the circle artwork above the placed image in that new file (I colored it light gray just so we can see it)

enter image description here

  1. select both objects on your art board. In your transparency panel, click “Make Mask” with invert mask option selected

enter image description here

Using the “place” with “link” option selected, at any time the original vector gradient Image can be edited and saved. These edits will update and appear in your new current document you are working in. The result is a much smaller file size in your working document with much less processor resources being used

Attribution
Source : Link , Question Author : Abeer Sul , Answer Author : wch1zpink

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