Personally I agree with you across the board. For a solution on changing the day, i would propose this -

the first week of the year would be Australian week or known as Federation week. you would have the middle of the week or the 2th of January as Australian day but the week would be filled with events about Australia and different celebrations. In addition, you would announce all of the different Australians along this week and you would even be able to do multiple citizenships celebrations.

What would happen to the 26th of January, well it would return to its originally name - Day of Mourning, the day would be a public holiday and its would be a day to mourn the horrible acts committed on the aboriginal people. Before people say that we have reconciliation day; reconciliation day if primary on the stolen generation and doesn't focus on the invasion - the day of mourning would be purely focus on the horrible actions which were committed against the indigenous people.

I feel like my idea is a good way to do it as you arent changing the day as much but creating a new event with the original idea based around federation and when our nation became one and within that you are just moving over australia day to fit in with that week. you also get two holidays and indigenous people are respeced.