@Eric Bailyn
There are plenty of variables that need to be considered given you and your mom's financial situations and what makes the most sense. There is no one size fits all and multiple factors should be taken into consideration.
The most tax advantageous solution is to inherit the house from your mom on a stepped up basis.
If your purchased property has appreciated and you are taking the home sale gain exclusion and have no additional capital gains above the limit, you can set your basis on the property (consider property taxes on the price paid). If title trades hands, the county could reassess the home to market value and you may be paying double the property taxes your mom was paying on her own.
I would sit with a CPA and run through multiple scenarios and how it will impact your cost, basis, gift exclusion limits, and estate planning.
Another option is to keep the property in your mom's name and formally loan the amount needed to your mom to make necessary capital expenditures, she will only be assessed the additional improvements based on permits pulled to keep it below assessed market value decreasing property taxes. When she passes (hopefully not any time soon), you step up in basis in the property at whatever the market value is at that time.
If you buy the property from her for $555k, as you mentioned she is single, she can max out the home sale gain exclusion (305k basis + $250k exclusion) to effectively pay no capital gains. This does increase the assessed value and increases property taxes paid going forward. You may also increase the assessed value when you make the improvements at a later date. But at the $555k basis + $350k in additions/improvements, you will need to hold it until the property is valued at $905k before you recognize capital gains. Personal property does not benefit you at a loss.
As you can see there are multiple options to consider, if you get the sale through, you can tax plan with trusts to move the money she wants to gift you over time, or she can gift you the full amount using the life-time gift exclusion limits without you having to gift any back to her.