On your SWG, yes it is fine to just lower the output percentage and/or turn it off to keep your FC at the right level. I often run my pump 24x7 for leaf/debris skimming and I couldn't turn my SWG down enough to stop the FC from rising. It is common, and correct, for the SWG and pump to be wired to a timer so that the SWG can only be turned on when the pump is on.
Heat pump efficiency varies with outdoor temp. The warmer it is the more efficient it is. Efficiency means how close to rated output can it reach. Your heat pump is rated for 137k btu at some temp and humidity, maybe 80 degrees. They will usually have a rating at several different temps. The less heat in the air the less heat it can extract and the less it will heat the pool. It costs the same money to run the heat pump no matter the temp. What changes is the heat output. Thus, the efficiency drops. For easy math it is like this. 100k btu heat pump at 80 degrees, 80k btu at 60 degrees is 80% efficient at 60 degrees. It still uses the same amount of electricity to produce the 80k as it does the 100k.
Modern heat pumps can generate heat down into the 30s, 32 to 35 degrees. Older, more than 10 years ago, heat pumps didn't work well below about 50 degrees. Your heat pump will still heat your pool when it is 50 or 60 degrees outside. But, it won't generate as much heat for the electricity usage as it will when it is warmer outside. And running the pump at night through plumbing and filter exposed to colder outside air will also reduce overall heat gain. So, the question is can you generate enough heat only running during the day? Or do you need to also run at night?
There are times when we really want to swim and I run my heat pump all night and it will gain a degree or two. And other times when it is the same temp at 6 am as it was at 10 pm, which means it put heat into the pool because otherwise I would have lost a couple of degrees.
You have a relatively small pool and a relatively large heat pump, I think you will be able to keep it heated by running during the day and off at night.
My heat pump is 45k btu and my pool is 20k gallons. My heat pump takes about 3.7 hours to heat my pool 1 degree. Yours should be able to heat more than 1 degree per hour because your pool is half the size and your heat pump is more than twice as big. Keep some notes and you'll start to see some trends in your pool for heat loss and heat gain.