3 mini splits will do very well. You might need fans to push air in extreme weather but convection is enough 95% of the time.
Turning off central,window,mini split or any type hvac while at work then turning on whlie at home saves energy. That aurgument has been around since hvac was invented. The only way one can know for certain is do it both ways over a billing cycle then compare tempature days and energy consumed. I did,more than once.
Remember what Klem says "I Heard and They Said are often the biggest liars in town."

Thanks for the reply, klem. Where would you put the three mini splits? The LR, FR and master bdr? One of the guys we had estimate suggested we use a ducted system in the attic with ceiling vents in the 3 bedrooms and wall units in the LR and FR. Is that what you are suggesting too?
. Good to know that turning the systems off when you are at work made sense. Hoping it will be that way for us too.

I can't read the room labels but it appears one mini split in each of the three largest rooms would surfice. Deciding between central ducted and ductless is simple a question of whether some rooms are often used indivudaly or if intire floor space is either in use or not on same scedule.

build a heating system closet
fur down ducts within living space serve
rooms from fur downs.

I test ductwork & find an average 30% duct loss.
lose this conditioned air into the attic & it costs
more to operate...plus iaq issues.

spending the minsplit money on fur downs with a
central system...(heat pump?) would be the way
I'd spend my $$.

here in my hot humid climate putting ducts in
conditioned space is a good savings.

best of luck.

rater,here in North Tx Fox and Jacobs was useing furr down in thier homes 50 years ago. In the last 30 years I can't recall seeing a new home with furr down. I have hired furr down installed a few times where I was installing central heat and air up-flow in a hall closet of older homes. The majority of customers I suggested it to opted instead for venting through the attic. Based on those observations,I surmise that there is bias. How well is acceptance of furr down in you market?

I think the bias is largely cost, not so bad if you are
installing ducts in fur downs in a home that never had
ducts.
There is an architect locally that puts furdowns in
all his new construction homes. he is known for building
energy efficient homes. if it wasn't one of his selling points
(the savings we get with ducts out of hot humid attics) the
average joe on the street wouldn't realize anything out of
the ordinary. his furdowns are simply part of the design of
the interior. they compliment the style of the house, rather
than being obvious.

sadly, he is one of the few on the same page as myself.

it is mostly in existing homes that I'm involved in
moving both equipment into conditioned space.
in most cases we make an unvented foam sealed ..
semi conditioned attic..in other cases we seal the ceiling
to create a tight air barrier to the attic..and insulate attic
well (conventional vented attic with ins on attic floor)
then closet fur downs ...

as you know, the layout of the house has to lend itself
to the furdowns. you can do it simply...like in my house
where the only furdown not in a closet is across the kitchen wall ...and just paint it to match the wall. no one really notices mine at all. or you can make the fur down a stand out or part of a trey ceiling.

in my experience, it has to be the right homeowner, the
right house & hvac company that will either do the furdowns..or just set up for someone else to build furdowns.
everyone has to be on the same page.
it isn't the most popular install...but is by far the most efficient one.

here in hot humid La. there is a savings for getting ducts
& equipment out of extreme attic temps. as are in many
areas.

Weigh the cost difference between conventional split system and mini splits.

New ductwork to be installed?

How do you heat? What fuel?

IMO

Sorry to be MIA. We were away for spring break.
I had to look up what fur down meant as I had not heard of it before. Unfortunately, we do not have the closet space for that.
The splits are going to cost us about 6000$ more to install than the 8000$-9000$ range quotes for the Central Air. We heat with Gas-hot water radiators and have no duct work.
We crunched the numbers to run the A/C for only a few months a year and it looks like Central Air makes more sense.
I will post a different thread asking for help deciding between the different models we have quotes for.
Thanks