Write down your budget. Then contact an architect.

Doubtful you want to pay as much to do the “update” as it cost to buy the house.

Here is one that was altered.

Mansard Makeover - before and after · More Info

And the Before was a TON better. Yours is better too. Don’t remuddle. Change your attitude and accept it.

Don't get me wrong. I love my house the way it is, but I have gone thru two membrane systems in six years and am in a constant state of anxiety, wondering where my next leak will be. If it weren't such an issue, here in Western Pennsylvania, I would embrace it and run with it. Finding a roofer to work on it is nearly impossible as they are so uncommon locally (except for commercial spaces....and those guys don't care about residential projects). The last roof has created an issue that has destroyed the cedar in the back of the house, which the last roofer denies responsibility for. It has been a fight and I am tired of it.

No advice for you Amanda, but that really is awful. Mansard roofs are usually on old houses, but your house is contemporary, I think. So remuddling is less of a concern, if you get an architect involved. But changing the roofline will be a very expensive option. Did the roof ever function properly, without leaks? If it did, then the better option might be tracking down the best commercial roofer to repair. Not sure how you convince them to work on residential property - that may require contacts or a lot of charm, plus some restaurant gift cards.

If you've had two roofs fail in six years, you're hiring idiots. Ask the best contractors, architects and roofing supply companies in your area who they recommend for flat roof work. If you have to wait for a good company to get to you, then wait. If you have to pay more for a good company, then pay them. Whatever the hassle and cost, it will be much cheaper than changing your entire roof system.

Maybe just move.

I don't know what kind of membrane you have been using, but

I have a portion of flat roof that is like a badly pitched shower pan. It is surrounded by concrete block walls and has a drain that is slightly higher than the lowest point on part of the roof, so it holds some water.

They still gave me a 20 year guarantee against failure.

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Perhaps you could do a pyramidal "cap" on the mansard and pitch it slighly from the center to all four sides and maintain the mansard.