There are four versions of the Original S.E.X., none of which had film caps in the power supply. So this is not a stock build. That 10-henry choke isn't original either, nor does the original have any iron under the chassis. So it's a little hard to tell what you have.
That said, the original used two caps of 10 microfarads/450 volts. Assuming these are the power supply caps, your 22uF/500v electrolytics should work well. The ends soldered to the ground wire would be the negative, and the other ends soldered to the choke would be the positive ends.
Because it is an unknown modification of some version of the original, it's hard to know for sure what you have. If you can post a photo of the whole top and the whole bottom, we can probably figure that out.