And if you're just hoping to replace party A entirely with party C, FPTP is one of the better systems as long as you're not in a country where election laws are set up to ensure that the Democrats and the Republicans are going to win almost every election. But that's a question of candidacy laws and incumbent rights; changing the voting system in the US won't suddenly cause other parties to get elected.
Anyway, the fact that party A fucked it up and party B is fucking it up doesn't mean party A lacks incentives to improve it tomorrow. Perhaps they fucked it up because their leader was incompetent, and now that there's been a change in leadership they will be motivated to improve.
Finland has generally had 3 major parties ducking it out usually around 15-25% for each. 1995 was last time single party got over 30% of seats. Depends a bit on time which exact ones they were.
English wikipedia doesn't have the historic list, but Finnish does https://fi.wikipedia.org/wiki/Eduskunta#Kansanedustajat_puol... Divide by 2 to get the % (there are 200 members)
The only system that doesn't have voting negatives to me is one with a population of less than 10 where I'm sole dictator. Any population more than that and someone will get mad at me and kill me. Republics with some form of voting are the best option I know of for large populations of people who aren't "mind numbed robots" with no ideas of their own, and there is room to tweak the voting system. However they are still terrible for getting good results.
The tender approach for time limited monopoly was just terrible though and had no good incentives at all, and so I'm not really sure a government monopoly will be much worse.