Unfortunately the "loan mathematics" is in many cases a misguidance or a misdirection.
Obviously as an exercise in arithmetic, if you can achieve a higher return elsewise by 0.0001%, then that option is "better" (ie in theory you'll have a tiny number of extra dollars after the years in question).
That is all a non-issue. The amounts involved are trivial either way.
The only key factor is - are you part of credit-addiction society?
A ubiquitous, normal, widespread problem in our era is, in a word, "debt problems".
Huge numbers of folks get in to credit card debt hell, student loan debt hell, car loan debt hell, mortgage debt hell.
(As a socio-political matter, many sensible people believe this is actively due to and explicitly caused by the policies of the government-banking complex - IMO they're right.)
Note that you say ..
"If I really cinched my belt..."
It's worth considering that ... people from our grandparent's generation wouldn't even understand that concept. So, clinching your belt "as opposed to what"? The fact is you're in a massive amount of debt, not based on an asset - anything could happen good or bad with your new career, the economy, etc. Sure, work your guts out, spend zero, and pay it off ASAP.
Thus, in answer to your specific question,
"When I make the annual repayment, should I withdraw the minimum amount or should I take out as much as I can afford?"
A) first, realize that there is an overwhelming need to sensibly pay off deadweight debt - at all times and in all circumstances
B) do the calculation and see how much actual money you're talking about either way via the "scheme" of "investing elsewhere, etc". In fact: is it just a trivial amount of money which does not outweigh the overwhelming need to sensibly pay off debt? If so, totally forget the idea. Get the debt paid off.
Bearing in mind that vast numbers of people today get in to debt problems, you have to carefully ask yourself if that is an issue for you. You're soon going to be exposed to the total nonsense of car loans, and high-limit credit cards. I for example suffer tremendous addiction problems which run in the family; so back when starting out I sensibly realized I'd be a prime candidate to fall in to "debt hell". Thus I took and do take active steps via my accountants etc to ensure that can never happen. You might say "Hah hah, of course I'll never run up credit card debt or a lame car loan" but is it worth the risk (again, the calculation in question is a trivial dollar amount either way), when "of course" you should just pay off this deadweight debt as soon as possible?
(I think it's well worth remembering that in our era folks ubiquitously totally confuse deadweight debt, as under discussion here, with actual business debt on equipment. So, if I have a crane or something that costs X a year to service the debt and it generates Y a year in company income, that's an actual calculation on whether a debt is worthwhile. But you're talking about a pure deadweight debt, as if you bought a Porsche or lost money at a casino. Pure deadweight.)