Maybe the insurance payout is beyond dispute at this point but, if not, find a contractor that will give you a quote to repair this to the way it was before. If this is "substantially" more (i.e., how much is your time/the trouble worth) than the amount the insurance company is offering, you should go back to them and ask that they pay you the amount in the quote or find someone that says that they can do it for the amount they are offering. As long as the damage is covered, they have to pay you what it takes to get the entirety of the damage repaired, minus the deductible. (The catch is that sometimes they have limits buried in the terms and conditions... :/ ) You have the right to sue (or at least arbitration) if they don't resolve the issue. Be sure to record dates and names of people that you talk with.
(If I may ask out of curiosity, which insurance company is giving you grief? Feel free to PM me if you prefer.)
Now, you said that you wanted to make a change but you can work those with a contractor afterward and pay the difference.
Although this work may be doable by a DIY, I would want a carpenter contractor to do all of the structural work and would insist on permits and an inspection. The contractor might even insist on having an engineer sign-off. If so, I would do it. It is always best to have those things done by book so that problems should not arise, and your insurance company doesn't have an excuse to refuse paying. As
@havasu was saying, you can always do the insulation, drywall, painting, etc. afterward. I've found that many contractors simply don't want to bother with some of those tasks that are not their specialization.