My thoughts.
I used to work for a major FTSE company.
I was able to pay to upgrade to CE for European flights although there was sometime an issue when the cheapest fare in CE was not as flexible as ET. I did not have any issues and sending the cash to some account worked.
I now work for a much smaller company and when I asked if I could pay to upgrade for Europe flights, I was told 'No' and it caused a minor drama with the CEO involved. As a 'third line of defence employee', he did not want anyone to think I was being given special treatment, even if I paid for the difference.
On a few recent work trips to FRA and LIN, I have paid to upgrade but it changed the flexibility of the ticket and luckily it was not an issue.
I would suggest that the OP bear this in mind.
My head office is a long haul flight away and I will be in J if I travel there, so not an issue, although there is a risk of a non OW carrier!
I would upgrade again at check in, and call the corporate TA to save them contacting my company when they receive the change email from BA.
Was I impressed that the CEO said I cannot pay to upgrade? No.
Does it make a major difference to my life, especially as I can upgrade from time to time? No.
The company pays me quite well and I do not travel that often, as well as being more advanced in years, so no issues.
If I was a lot younger and had to travel Y LH all the time, I would certainly consider the overall package.