I could have written your post word for word about nineteen years ago when I was trying to wean my now twenty year old son (who, incidentally, is now over 6 ft, and fit and healthy). I could write a book about the traumas I went through. I used your same words - 'he'll only eat beige food', and people still ask me 'does he still only eat beige food?'
For many years all he would eat was chicken nuggets (I made my own and froze them in batches), toast, petit filous yoghurts (no other brand), rice, pasta, chips (only thin ones), cheese (only mature cheddar), eggy bread (or french toast), pizzas and fish fingers.
I tried literally everything everything, starvation, bribery, cajoling, punishment, incentives - you name it. It had such a negative impact on our lives, and no-one really understood and I felt terribly criticised
Eventually, we saw a nutritionist and a behavioral psychologist and they both agreed that he was getting enough range and as he was growing and was healthy that I should feed him what he wanted. So I did and our lives improved dramatically. We had strategies for dealing with social situations such as taking a packed meal when we were invited to friends for lunch, and choosing restaurants with great care when eating out.
Punishment didn't work - in fact, in our case nothing worked - it was him making the choice to change things that in the end made the difference. This first happened when he was about 16 and started going out with friends. I was jaw dropped when we took him and his brother to Nandos on holiday as a treat and watched as he ate a chicken burger dripping in hot peri peri sauce. He told me that the first time he ordered this meal with friends - he didn't know it would have sauce on but forced himself to eat it because he didn't want to look foolish in front of these kids.
Cut a long story short(er), he now eats much better (he is completely tee total so it does have some benefits) although his diet is still fairly limited. I just wanted to let you know that I really do empathise - I've been there and I know how difficult it is. Good luck