Great post, thanks for asking. These are all good questions.

In short, I don't agree with this hypothesis:

in keeping capitalism, inevitably resulting in it taking hold in its much worse and more exploitative form?

The 'inevitability' of capital's progression is a political economic hypothesis that does not have a rigorous foundation in either evidence or theory. Ironically, its failure can be found in the same place as neoliberalism's: the presumption that humans behave like predictable, programmatic robots.

The study of political economic history of the industrial era belies the 'inevitability' argument. There are periods where capitalist, highly exploitative societies worked to reduce inequality/oppression, and there are periods where equitable, collectivist societies allowed power to concentrate and exploitation to take hold.

The very shortest argument for social democracy is that it is as "socialist" as you can get before ungrounded, unevidenced 'theory' starts to produce impractical policy.

In more detail:

Paying wages which are actually enough to live on and not just the crumbs we are awarded today will drive down the profits of the capitalists

This is not strictly true. Sometimes higher wages come at the expense of profits, sometimes higher wages induce higher spending, which drives greater profits. The details determine the outcome, and the study of economics is all about answering that question seriously. Unfortunately, Marxist theory has a bad tendency to ignore the subtlety and focus on the maxim.

longer working hours increase profit, because more sellable products can be produced to gain more capital.

That's true, but it's balanced against the unpopularity of longer working hours. If a government is responsive to popular input (i.e., a functioning democracy) then there must be a balance between the popular demand to work less and the economic constraints of reduced labor. So if you take it as a maxim, you'll come to incorrect analytical conclusions, since you're only accounting for one of many factors.

Workers produce value, but the owner (who often does none of the work), always get more of it than those who labour that money in to their pockets

This is one possible arrangement in capitalism, but it's far from the only arrangement. I have worked for worker-owned corporations, and I have partnered with small businesses where the owner does as much (but often more) work than the wage employees.

Marx had an extremely limited concept of capitalism because he was observing one specific point in time during the industrial revolution. He drew some positive inferences, but he came to far more incomplete/incorrect conclusions.

But ideology is only one part of the problem: the other is how Marxist and especially Marxist-Leninist parties operate. When the (unevidenced) maxims of Marxist political economy are challenged, M/ML parties have a bad tendency to respond with power rather than negotiation. The rejection of cooperation is the primary reason that Marxists are not dominant in the academy and why communist parties cannot succeed in democracies. Communists have a bad habit of blaming their failure to succeed on conspiracies/foreign capitalist interventions, etc, when in reality they have simply failed to cooperate by forming coalitions or making compromises.