So after much searching around, I found the answer uses iptables, setting up a NAT, and using the built-ins PREROUTING and OUTPUT.
First, you must have port forwarding enabled:
echo "1" > /proc/sys/net/ipv4/ip_forward
Then you have to add the following rules to your iptables NAT table, using your own values for ${P_src} and ${P_target}:
iptables -t nat -A PREROUTING -s 127.0.0.1 -p tcp --dport ${P_src} -j REDIRECT --to ${P_target}`
iptables -t nat -A OUTPUT -s 127.0.0.1 -p tcp --dport ${P_src} -j REDIRECT --to ${P_target}`
If you want to remove the rules, you simply need to use the -D switch instead of -A for each rule.
I build a nice little script for this that does adding and removing of mappings.
#!/bin/bash
#
#   API: ./forwardPorts.sh add|rm p1:p1' p2:p2' ...
#
#   Results in the appending (-A) or deleting (-D) of iptable rule pairs that
#   would otherwise facilitate port forwarding.
#
#   E.g
#   sudo iptables -t nat -A PREROUTING -s 127.0.0.1 -p tcp --dport 80 -j REDIRECT --to 8080
#   sudo iptables -t nat -A OUTPUT -s 127.0.0.1 -p tcp --dport 80 -j REDIRECT --to 8080
#
if [[ $# -lt 2 ]]; then
    echo "forwardPorts takes a state (i.e. add or rm) and any number port mappings (e.g. 80:8080)";
    exit 1;
fi
case $1 in
    add )
        append_or_delete=A;;
    rm )
        append_or_delete=D;;
    * )
        echo "forwardPorts requires a state (i.e. add or rm) as it's first argument";
        exit 1; ;;
esac
shift 1;
# Do a quick check to make sure all mappings are integers
# Many thanks to S.O. for clever string splitting:
# http://stackoverflow.com/questions/918886/how-do-i-split-a-string-on-a-delimiter-in-bash
for map in "$@"
do
    IFS=: read -a from_to_array <<< "$map"
    if  [[ ! ${from_to_array[0]} =~ ^-?[0-9]+$ ]] || [[ ! ${from_to_array[1]} =~ ^-?[0-9]+$ ]]; then
        echo "forwardPorts port maps must go from an integer, to an integer (e.g. 443:4443)";
        exit 1;
    fi
    mappings[${#mappings[@]}]=${map}
done
# We're shooting for transactional consistency. Only manipulate iptables if all 
# the rules have a chance to succeed.
for map in "${mappings[@]}"
do
    IFS=: read -a from_to_array <<< "$map" 
    from=${from_to_array[0]}
    to=${from_to_array[1]}
    sudo iptables -t nat -$append_or_delete PREROUTING -s 127.0.0.1 -p tcp --dport $from -j REDIRECT --to $to
    sudo iptables -t nat -$append_or_delete OUTPUT -s 127.0.0.1 -p tcp --dport $from -j REDIRECT --to $to
done
exit 0;