The window will need to be replaced eventually anyway. So, I might as well replace it with something that works better.

I think a window that opens top down like this:

with window covers that open top down would allow air in without covering the window in a way that hides the fact the window is open. Not covering the open section also makes the ventilation more effective since it isn't blocked by window coverings, yet a the same time you still have privacy below if you keep the bottom section covered. Seems ideal.

The only issue I see with this is that I still need bug screens that will cover the window whether it has been slid open from the top or bottom.

The windows would generally be opened only from the top when opened for air ventilation. I assume the windows must also open from the bottom for fire escape safety.

The only other option I can think of is installing a mini-split a/c in the bedroom and just keeping the windows closed 24/7.

Since you have a slider now; that suggests the window might be wider than it is tall, in which case you might replace with an awning window that hinges at top; the most rain-resistant type you can get (notice I didn't say rain proof).

Ceiling fan to reduce the need to open the window, and light weight curtains that move with the breeze.

It's close to square. Roughly 46" h x 48" w.

There is already a ceiling fan.

I am surprised that no one has suggested an alarm system. I live in a safe neighborhood in a small town without much crime, but it is an open invitation to a thief to leave a first floor window open when no one is at home.

I purchased a non-monitored alarm system.

With door and window sensors, you will see that something is open when you leave the house and you can't set the alarm until you have closed the windows and doors.

The alarm sensors won't help the issue of the wood window sills getting wet when they fall asleep with the sideways sliding window open when it starts raining during the night.

Top opening windows would eliminate most of that issue. A few drops from the top of the partially open double hung window won't be enough to damage the sills.

Finding a way to keep the room at a comfortable temperature that matches the rest of the house without opening the window would eliminate it.

There are so many hypotheticals to your dilemma.

Is the occupant a fully functional adult? Make it clear that if there is damage due to rainwater intrusion, the bill will come to them.

Apart from that, the post it/cell reminder/Alexa reminder/alarm system should be sufficient to help them remember. Replace all the windows when they actually need it. Perhaps the shutters can be sealed with a sealant suitable for outdoor use.

If the occupant is a child or someone with head injury or developmental disabilities, you will more than likely be responsible for double checking all sorts of things for as long as they live with you.

Jaxo, seems like you already know what you want. 2 double hung windows, with a full screen. I'd get them in full vinyl to be the most water friendly since I suspect if the person can't close the windows now, the new windows won't change that fact.

Do they make double hung windows with smaller frames?

Look at the massive difference in the the 2 pictures I posted. The bottom picture looks almost exactly like the windows I have and the top picture is how the only photo of double hung windows I could find looks. The giant bezels don't match the rest of the windows in the house.

"The giant bezels don't match the rest of the windows in the house."

Well yeah, that can happen when you're only replacing one window out of a whole houseful. It can look off. Have you called any window companies?

The opening can be framed for a smaller window. The wall will have to be repaired and matched, inside and out. You may or may not be able to get a window that matches the styles of the others. And it will affect the fenestration. Which is why a simple solution to remind the person is maybe better and certainly less costly.

There is only one window on that side of the house. So, it doesn't need to exactly match any other windows and, of course, it can't exactly match since it has to slide vertically instead of horizontally. However, I would still want it to have the same basic style as the others with similar width frames as the rest of the house.

Is there there anything about double hung windows that requires them to have thick frames like the photo I posted?

You want the same window style, meaning Florida windows are out so ...

https://imgur.com/7xGlxD6

Just kidding.

Perhaps something similar to a Juliet balcony covering most of the window:

http://www.caldergates.co.uk/wrought-iron-bowed-juliette-balcony.html

Some could enable you to add flower boxes as well:

http://www.atspeed.co.uk/juliet-balcony.html

Casement windows hinged at top. Maybe add a artscape window film for privacy without need for any shades, curtains, etc.

Your 4 years to late, casements hinged at top are awnings.