Would improving SWR necessarily improve reception gain figures?
Yes, high SWR affects digital reception way more than analog reception. Holl_ands has a long discussion of why some where in this forum.
We are assuming that the raw feed point value is 300ohms. Maybe the 4:1 balun is not going to perfectly balance the impedance at any point.
Impedance varies with frequency. The SWR is the impedance mismatch from 300 ohms (which is a setting in the 4nec2 program). The further away from 300 ohms, the higher the SWR, ie the Impedance mismatch. Because Impedance consists of real and imaginary resistances, it will take time to figure out the best impedance value for this antenna. Then if you wanted to, build a custom coax balun for it to connect to a 75ohm coax downlead. (Most ham coax is 50 ohms).
The SWR mismatch also effects Net Gain.
A quick way to look at the SWR figures to subtract from Raw Gain :
SWR Mismatch Loss dBi
Two way radio SWR should be less than 1.0
No, no, SWR is a ratio. 1 to 1 is the best you can get. If your meter had a zero setting, then that would have been 1:1, which would correspond to 1.0 in our context. A lot of older equipment used general purpose meters, whose scales would run from 0 to 10, 25, 50, 100 etc.