I think you are being overly pessimistic if you don't think those problems can be solved in less than a few years for less than a couple billion
Of course, I am calculating towards the pessimistic there. I rather consider it realistic. Its easy to assume that everything will work perfectly at the first try. But in reality even a genius won't achieve this too often. Or many of those.
So: It takes years to develop a car. A car is now nothing too special, we have build millions before, and we are developing cars already for 100 years. A new car model family is already a multi-billion investment (The MQB/MPB system of Volkswagen for example, which not only modularized the car development for a large number of models, but also standardized the car production tools for multiple factories and brands).
A LM 2.0, regardless that we have already build one before, will be a technologically more challenging project than a new car. Instead of just pleasing government regulations :dry: or increasing customer standards, we have to make it spaceflight capable and please increasing customer/investor/politician standards.
Soo, where could you cut development costs? We maybe can simulate more today, but we also know more about space and moon today to consider in the planning. Even if it won't cost 3 billion for just doing the same as the LM with the same number of spacecraft - you won't get it for 500 million. About 1.5 - 2.0 billion USD sounds like a good ballpark figure for me for 6+1 two person spacecraft. One billion would be possible with some optimistic assumptions - for example being able to not require (too) special tooling to build the spacecraft. Just building one spacecraft would not work, you would need at least two, a flight article and a (flight) prototype.
And then, the pure construction costs for just one such spacecraft would sure not be 1 million. If you can build it as large aerospace company between other projects (so most of the fixed costs could be avoided and labour force would be no big problem to allocate), about 30-50 million sounds reasonable. If you are a small specialist company (like Grumman), the fixed costs would inflate this and such costs exceed the pure costs for materials and COTS components by far. You won't be able to build such a spacecraft with a small team - you need quite a number of specialists there and a good number of less-specialized hands.
Soo - could you imagine pushing the costs even below 800 million? 800 million would still be a major project for a government and would result in major political fighting - even in the ruling party. And finding investors for 800 million USD with some high chance of failing to stay in this budget would even be hard for Elon Musk.