Yes, I’ve noticed that already years ago on another custom signet network.
Now rebroadcasting every 30 seconds.
~ $ cat bin/rebroadcast-all.sh
#!/bin/sh
lock=$PREFIX/tmp/${0##*/}-$(echo ${PWD} | md5sum | cut -b-8)
test "$1" = "-c" && { rm -rf $lock; exit; }
mkdir $lock >/dev/null 2>&1 || exit 1
echo Rebroadcasting transactions from the mempool...
{ grm.sh \
| grt.sh \
| sert.sh
} >/dev/null 2>&1
echo Rebroadcast done
rmdir $lock
First it gets raw mempool (grm), then gets raw transactions and finally it sends them raw. One by one.