Keep it simple.
It’s obvious that the truck fits no problem. So assuming you are reversing on your good side, simply try and present the trailer as straight as possible in line with the dock. The best technique in my experience is a ’ late ’ and more pronounced turn.
Some call this ’ jacking ’ it in (presumably from the term ’ jacknife '). As the wise sage Juddian advises- seek every opportunity in a quiet area of a motorway services or your/customers yard to practice this method. Once mastered, you will be amazed at how little space is required to present the trailer into tight spaces.
The fear of reversing into someone’s cab as they are reading their paper is quite understandable for newer drivers, but once this late turn method is adopted, it will build your confidence. ANY doubt at all, handbrake on and go and have a look. I personally am always impressed when I see a driver getting out and checking. That in itself shows professsionalism which is becoming increasingly rare.
Blindside reverses are a different animal and if you HAVE to do one (no choice in some yards), always ask another driver to help. ANY driver worth their salt would be only too happy to oblige.