I could only pull this off if management saw benefit. What possible
points could I provide to increase my chances?
In your question you spent a lot of words explaining why this arrangement would be good for you, but none about why it will be good for the company. Focus on the company when you ask for an accommodation. While they may be happy for you, and supportive of your motives, from the business/management side they still must consider "what's in it for us?", "how will this impact us?" and "what do we do about it?"
First, point out the benefit to the company of your having an additional half-year of education. Explain what you will be learning that you don't already know, and how those subjects will make you a better employee, more productive, and more effective.
Second, point out how you can continue to be very productive in your current job - even while working remotely, and even at a reduced workload. Point out where your past work demonstrates how you can be trusted to work remotely, explain your plan for how you intend to stay in the loop on all necessary information, talk about how you will effectively attend meetings remotely, and how you will update your boss on your status despite being remote and despite any time differences.
If it's true, explain how the time difference will work to their advantage. Explain the kinds of things you will be able to handle in your time zone, that will help others in the home office be more effective.
Hint (but don't directly state) that you will have to leave if your accommodation isn't accepted. You don't want to blatantly threaten here, but just want to indicate that you definitely intend to study abroad one way or the other. Explain how this accommodation will keep you around as a loyal employee for the long term.
Avoid bringing up the "I consider myself to be underpaid" angle. It's not relevant to this accommodation, and could easily derail your discussion. Focus on your 1/2 year plan. Deal with your pay in a year or so, once your education is complete.
As JeffO astutely suggests, you could even offer to work a few days remotely now, in order to demonstrate to the company that you can be trusted and effective working remotely. Doing it now gives them a chance to experience what it will be like during your studies - perhaps even before they commit to your accommodation.
If they are as shocked as you think they will be, you may have to talk with several folks and be very convincing. Think this through ahead of time from their point of view so that you can have as strong discussion topics as possible.
And of course be prepared to leave gracefully if it doesn't work out as you hope.
Or as The Wandering Dev Manager correctly suggests, you could ask for a 6-month sabbatical. If you are currently an excellent employee, your company may be willing to grant that concession.