I do not think that this is correct. There is no published fare at £400 or £700 return on AF/KL/DL that does not involve a Saturday night stay, whether with zero, 7, 10, 30, 50, 60, 90, 150 or 300 days advance purchase.
Moreover, even last week, we would still have been past the 50 day advance purchase period so that would not have explained a rise this week.

It is possible that there might have been a promotional sale that did not require a Sat night stay which has ended; it may well be that the JV has changed the minimum stay requirements on cheap fares (I doubt it as I seem to recall such rules before but I may be wrong). It may be that the OP mistaken entered other dates without realising it, etc... I don't know but two things are very clear:
a) there is currently no cheap tatl fare on the AF/KL/DL JV that does not require a sat night stay
b) given that ST has no dominance on the EDI-MIA route or, globally, on the tatl market, this can hardly be described as an abuse of market power: there is more than ample competition on EDI-MIA or tatl routes generally. As you suggest, the OP may make use of that ample competition to buy a ticket on an airline offering a considerably cheaper fare to those offered by ST airlines for his travel dates.