How can I modify this bash script so that the port argument is optional?

I often connect through ssh to Docker containers running on a remote server. Every time the container is stopped or removed, I need to copy my ssh key on the container again, in order to connect. For this reason, on my Mac laptop I put this simple bash script, whose goal is simply to add my ssh key to the Docker container to which I want to connect.

#!/bin/bash

# A POSIX variable
OPTIND=1         # Reset in case getopts has been used previously in the shell.

# Default parameter value:
PORT=...
PUBKEY=...
HOST_IP=...

# show_help function
show_help() {
    echo "Usage: $(basename "$0") [-h] [-p PORT] [-f PUBKEY] [-i HOST_IP]"
    echo
    echo "   -p PORT           add key to container running on port PORT (default: ...)"
    echo "   -f PUBKEY         add key file PUBKEY (default: ...)"
    echo "   -i HOST_IP        connect to host HOST_IP (default: ...)"
    echo
    return
}


while getopts ":h:p:f:u:" option; do
  case "$option" in
    ?)
      echo "invalid argument"
      show_help
      exit 1
      ;;
    h)
      show_help
      exit 0
      ;;
    p)  PORT=$OPTARG
      ;;
    f)  PUBKEY=$OPTARG
      ;;
      ;;
    i)  HOST_IP=$OPTARG
  esac
done

shift $((OPTIND-1))

USER_AT_HOST="root@$HOST_IP"
PUBKEYPATH="$HOME/.ssh/$PUBKEY"
ssh-copy-id -i "$PUBKEYPATH" "$USER_AT_HOST" -p "$PORT"

exit 0

I have two problems:

(smaller) the arguments have non-intuitive letters (f for the PUBKEY, i for the HOST_IP) because if I’m not mistaken, getopts only support single-letter arguments. Is there any way to circumvent this limitation? If not, could you suggest some more creative/self-explanatory letters for the arguments? 🙂
(bigger) currently the -p argument (PORT) is mandatory, and the user used for the ssh connection is always root. I would like to modify the script so that, if the -p argument is not passed, then another argument -u (USER) must be passed, and the connection command becomes
```
 USER_AT_HOST="$USER@$HOST_IP"
 PUBKEYPATH="$HOME/.ssh/$PUBKEY"
 ssh-copy-id -i "$PUBKEYPATH" "$USER_AT_HOST"
```
instead than
```
 USER_AT_HOST="root@$HOST_IP"
 PUBKEYPATH="$HOME/.ssh/$PUBKEY"
 ssh-copy-id -i "$PUBKEYPATH" "$USER_AT_HOST" -p "$PORT"
```

How could I modify the script in order to obtain this result?