A couple of days ago I stopped into a Braber shop and talked with the owner. He has a very heavy beard and has been shaving since the age of 13. His comment was that there are three key elements to a good shave. A sharp razor, not knife sharp but razor sharp, stretching the skin, and hot towels. He uses 5! towels on himself and his customers.
Since you are not showering before your shave then you really need to focus on getting your whiskers saturated with water. There is no shortcut for this.
Next, get the razor checked out by one of the members here. If someone has not already sent you there address then let me know and I will help you.
The hanging hair test is shown below. The razor is held steady, only the hair is moved downward over the blade, root end out about 1/2 inch. It should cut the hair with no problem at all.
I use 35-50 roundtrip laps on the linen first then the same on the plain leather strop.
Hope this helps, :)