Judiciary! I am ignorant as to how the Roman courts worked, I realize that there was a split between Senate trials and the common law courts but I think the problem of bribery may have been the bigger problem than their independence from the Senate. (If that is what you are suggesting.)
truly a problem that had to be addressed but I won't even try to address that problem here, I have nothing but the common cliche solutions to offer.
The problem with the judicial system was that it was run by senators. Not the senate at-large of course, but every judge (or praetor) was a senator, who could go on to serve as consul, or any number of roles in the senate. Julius Caesar for example, was praetor in 63 BCE, and every consul had to serve as praetor first. For this reason, the role of praetor was heavily politicized, and this made judicial corruption inevitable. In modern democracies, a strong and independent apolitical judiciary is one of the cornerstones of stability and the rule of law, and without that, the praetorship helped doom the republic (especially after praetorships became a prerequisite for a command in the provinces). Bribery is only really possible to reign-in if there's an independent judiciary without major interests tied to the senate (which were usually the ones doing the bribing). Julius Caesar, for example, payed huge bribes to get elected to the praetorship, and if he enforced the bribery laws on the books after his election, the praetors for the next years would bring down the fully legal might of the senate upon him for his hypocrisy. For this and other reasons, judicial independence was really impossible, and contributed heavily to the fall of the Republic. The sacrosanctness of tribunes was so fragile for the exact same reason (i.e. it was impossible to enforce due to conflicts of interest from the judges themselves).
No doubt the lack of a check on proconsular power was the biggie
I agree, and I think this really is the central issue. If this remains unresolved, all issues of income inequality, judicial independence, and the patron-client system are totally tangential, since after any attempt at reform, any general can simply unravel the whole effort through force of arms. All laws in any society are ultimately backed up by the implicit use of force, so by definition the Republic was dead when the senate gave control of armies to proconsuls. The only way for this to be resolved is to either a) centralize the military under the reigning consuls or some other apparatus, b) create some check on the power exercised by proconsuls in the provinces, or c) avoid expanding outside of Italy. However, the Roman concept of imperium (the idea that magistrates had power over life and death and were immune from prosecution as long as they were serving the state) pretty much precludes any direct checks on proconsuls beyond just sending two proconsuls to every province. This is what I mean when I talk about institutional unbalance. Even if, hypothetically, the senate abolished the patrician/plebeian distinction, redistributed land to the poor, and eliminated the patron-client system through welfare, it could all be undone by any rogue proconsul with a big enough army. We agree on the broad strokes of what killed the Republic, we just disagree on what the central issue was.
But I fear the manner in which the empire expanded so quickly during that century, and the great distances involved made the rise of these 'great men' inevitable
Well yes, that's a fairly common view among historians. Conquering the Mediterranean was like swallowing a poisoned pill, and was largely responsible for destroying the Republic. However, this is only due to the institutional fragility of Rome. It's not directly impossible for large states to exist as republics, but if the republic in question isn't equipped with stable enough institutions to handle the inevitable consequences, then it will go the way of Rome.
But I must admit I am not sure even now how you reign in such power when you consider the tasks these proconsuls were expected to perform
The same way we reign in proconsuls today. After all, General Eisenhower didn't march on D.C. when he returned victorious from Europe in 1945. A strong judicial system, a clear and centralized chain of command, and respect for the rule of law backed up by the credible threat of implicit force. The Roman Republic didn't have these because no ancient state had these until the Empire came about, and the institutions of the Republic didn't change quickly enough to accommodate for the emergence of the generalissimo in the 2nd century BCE.
In conclusion, I don't think income inequality and class issues were unimportant, but I think the Marxist-esque reading of history that sees the fall of the Republic through a classist lens is a bit off-base because it misses the root of the problem, namely the fragility of Roman institutions and imbalance of the political power structure.