I had many of the same problems when I started just a few years back. Nowadays, I can get a smoother shave from my Dovo steel SR than with a disposable SR, though my double edge razor is slightly easier on one part of my face (immediately under my chin), but worse on others. I shave WITH the growth first, and then across (sideways). The problem area under my chin gets smooth after three sideways passes, but this feels uncomfortable if my blade is not perfectly stropped.
So, I found my biggest problems could be solved with stropping:
1. I have a fabric canvas strop. I use this before every shave (just five strokes). It is indispensable. I simply could not keep my blade sharp over several shaves without it.
3. Your main strop should be nice and smooth. I did not strop for long enough before, but more strokes is generally better (I never counted, maybe I should do that next time). I have a wide strop and a narrow one, but I actually prefer the latter, as the x-pattern seems to work better on that one. I finish with some very light strokes on the strop.
2. When the blade tugs too much and is getting dull: get a diamond paste for a separate sharpening strop OR (better if you ask me) use a very fine water stone, build up slurry, and apply a little of this slurry on the sharpening strop. It works even better than paste in my experience. I only use it now and then, but it is important to have when the blade is slightly dull, it can make the blade very very sharp. If the blade is getting seriously dull, hone the razor on the water stone first.
It took me a while to figure all this out, and I suppose that my stropping and shaving technique also got better, but now my relatively cheap black high-carbon steel Dovo can give an absolutely baby-smooth shave.
Good luck!