How to improve insulation in a single room
Your #1 enemy is solar gain
The southwest location of that room is the major problem on keeping the room conditioned to spec.  It catches the brunt of the sun, which affects south more than north (for obvious reasons), and affects west more than east (because the east side of the house is still cold from the night).
This means the house's balance completely changes hour by hour.
I hope you're pausing to consider what that means...
&quot;Wait.  So if I have a one-zone heating system with one blower, that distributes heating to different rooms via ducting... and that ducting balance is tuned either by design or by adjustable flaps... and that is the normal setup for most homes... that is imbalanced half the time?
Yup, that's what I'm saying.   Not half the time exactly, it might be balanced for sunless times, in which case the sunny rooms are &quot;too warm&quot; but the rest of the house is right.
It gets a lot messier if the thermostat is located in a sunny room.  Now you have the tail wagging the dog: the thermostat is treating its amount of solar gain as if it's heating the whole house.  So solar gain makes the rest of the house get colder!
Solar gain is around 340 &quot;BTU&quot; per square foot that is straight-on to the sun.  So if the sun is at a 45 degree angle to the wall/surface, that means 340/sqrt(2) or 240 &quot;BTU&quot; per square foot.   Regardless, we're talking a lot of heat gain.
When I say &quot;BTU&quot; I mean the HVAC industry unit, which is actually BTU/hr.
Insulation will only help somewhat.
Insulation will reduce overall heat gain/loss... somewhat... but it cannot eliminate the fact that south and west will catch a lot of heating from the sun.  The balance of a 1-zone house will still be thrown off.
The only way to really balance it is to have a multi-zone setup, or have an auxiliary  heat pump just in the room which adds heat or cooling as needed.
The cheapest way to keep the room consistent is to place the thermostat there.  Of course that'll be the tail wagging the dog, and the rest of the house will take a wild ride.