it is a nice question and you posted nice code and had back interesting and wise answers.. but when I see so simple tasks I cannot resist to try a oneliner solution ;)

perl -e "while($ARGV[0]<=$ARGV[1]){$t=scalar localtime($ARGV[0]);print
+ $t.$/ if $t=~/\s1\s/;$ARGV[0]+=86400}" 1580500427  1591220427

Sat Feb  1 20:53:47 2020
Sun Mar  1 20:53:47 2020
Wed Apr  1 21:53:47 2020
Fri May  1 21:53:47 2020
Mon Jun  1 21:53:47 2020
[download]

it is not bugged for year 1 ;)

L*

PS shorter

perl -e "$t=shift;while($t<=$ARGV[0]){print gmtime($t)=~/(.*\w  1)/?$1
+.$/:'';$t+=86400}" 
# or
perl -e "$t=shift;while($t<=$ARGV[0]){print gmtime($t)=~/(.*  1)/?$1.$
+/:'';$t+=86400}"
# or
perl -le "$t=shift;while($t<=$ARGV[0]){gmtime($t)=~/(.*  1)/?print$1:0
+;$t+=86400}"
1580500427  1591220427

Sat Feb  1
Sun Mar  1
Wed Apr  1
Fri May  1
Mon Jun  1
[download]