That yellow "paste" is just grease for condition the leather side of the strop. To be applied very sparingly, once a year or so. Or even better, not at all. If you regularly rub the leather with your bare hands, the natural oils from your skin will keep the leather in top condition.

The edge on your razor might not be lost. It probably just requires an efficient stropping. First you need to remove all the yellow paste from your linen. Put a few layers of kitchen tissue paper on top of it and a double sheet of newspaper. Then run a hot iron over it, refreshing the tissue paper regularly.

When the linen is clean again, strop 60 laps. Your method sounds good. You need some speed during the stroke. Flip the razor as slow as you want, but do apply some speed during the stroke. Pressure must be light, but enough to have some friction going on.
Repeat those 60 laps on the leather strop, same fashion.

Let's see if that re-awakens the edge.

Best regards,
Bart.