While I agree Maria Fyodorovna was not overly enlightened on politics and other affairs, overal I do not agree with your view on how significant her faults and ill choices were in the fall of the Empire.
I cannot really comment on how much she knew about corruption in the Red Cross, or her investments in mining operations, since I have no knowledge on that, but Grand Duke Sergei was HUGELY unpopular for being stern, to the point of being perceived as cold-blooded and cruel in the public mind, for various reasons, not the least his part of blame for the Khodynka tragedy, allowed by him neglecting his duties. Even if there were not rumours about his corruption, the public would have reacted the same way to his assasination, and he would be assasinated, even if only for the sake of the post he held.
As for her bad relationship with Alexandra, both women tried getting on at first, but their utterly different characters as well as pigheadedness made any attempts of reconcilication impossible. The argument over jewelry can be put down to Maria Fyodorovna´s vanity, but I don´t think it hurt the prestige of the monarchy too badly at all. As for the dispute of precedence, has it not been sorted by a tsar much before Nicholas II´s time? Maria Fyodorovna, in this case, had protocol on her side.
Maria Fyodorovna, as a wife of the Tsar, knew perfectly well how exhausting a job ruling was, I am sure. And as much as I sypathize and understand that Alexandra in her poor health and worry about Alexei could hardly lead society, the isolation in which she brough her family, was definitely extreme which actually DID help to damage the imperial prestige. Even when her daughters grew up and everyone expected them to, if nothing else, start attending social gatherings once in a while, Alexandra did not allow it. Also do not forget that Maria Fyodorovna, at last for a time, did not know Alexei had hemophilia.
As for the gossip and rumours, it was Maria Pavlovna´s court, which was the main source of it all. Maria Fyodorovna did lead her own little campaign against Rasputin, who she honestly believed a dangerous fraud, but she did not spread rumours about him and his lecherous doings in the palace, like others did, because she knew better. She despaired over Alexandra´s refusals to listen. Had she defnded her son and daughter-in-law in the matter, it would have only done harm to her as well, not salvaging anything, least of all the whole monarchy, that was slowly rotting anyway - at least that is how I see it.
I agree her matchmaking efforts were disasters more or less, she certainly did not have her mother´s talent when it came to it, but I would not agree with the statement that she should have find Mikhail a suitable bride. He was a responsible adult and he chose to marry Natalia. How was that her fault?
Maria Fyodorovna was arguably the most popular and loved Romanov amongs the whole family, popular with both society and public. Yes, perhaps she could have done more - but what? When she came to Nicholas with a sensible advice, or recomended people to him, he did not listen. Yes, she was not willing to give up the glittering lead role in the society, then again Alexandra has no interest at all to seize it. Yes, Maria Fyodorovna was proud and vain, but she had social skills and perceptiveness, and enough intellect.
She had her part in the decay of the monarchy perhaps, but her share is nothing compared to actions of other Romanovs.