Ok, this will be a long answer for a long question.
Strategic consulting and most Fortune 500 companies operate at very different speeds, and moving from consulting to the industry will be shocking, at least in the beginning. The industry feels slow, and not assertive, decisions take way longer to be taken, most of the times there is an unspoken desire to have a full agreement before taking tough decisions.
So, in my opinion, it is not a downgrade just change of scenarios, with a change in pace and career progression as well, on the other hand, there is up or out rules in the industry.
I find it hard for the industry to be as exciting as consulting, you will also miss the mind-blowing problem-solving sessions from consulting. In the industry, this is much slower and less important than in consulting.
If you do it right and build the rapport that a good internal consultant advisor should have, it can become very influential, and soon you will be the unofficial advisor for several leaders, but again remember, the industry moves slower and will take time and dedication to get there.
I hope you do not become a back office employee, otherwise your future is gone, you need to be ahead of the game, deliver what has not been asked, predict what will come next and be ready, become invaluable for the leadership.