Hello Chris,
I use my Galaxy S8 smartphone for SD and battery life is also important to me.
I see exactly the same symptoms as you do if I turn the display off (GPS goes off-line).
However the GPS provides position data to SD within 1 -2 seconds of screen on, so no issue for me.
If my S8 phone is fully charged I get around 5 hours of SD use (display on continuously) before I need to charge the battery.
Tony