I'm no OSTicket expert, but you can achieve all of this rather easily with OSTicket.
The answer to all of your troubles is to create an email alias.
The from that the OSTicket uses will be seen in the email that the user receives.
That same user will reply in between the
===== reply =====
=== end reply ====
lines.
When the user replies, and sends the email to 'support@domain.com', that is actually an alias that emails your 3 support guys and then a 4th email to OSTicket under whichever address it monitors, this way a new ticket will be created appropriately.
Does this sound like something that would work for you?