Hi Chrissielizzie,
I can't help you I'm afraid. This will be my first time in Harwich. When I've turned up at Ferry ports before (with the exception of Dover), there's usually somewhere near the check-in booths to park up. I'm getting a 09:00 boat near the end of May and I believe this is the first boat of the day so I won't be getting in anybody's way.
The problem with Dover is that there is such a throughput of traffic, 24 hours a day, that they don't like people parking up until they're ready to board. Although the port at Calais seems to offer good facilities.
For me, going down the night before means I don't risk missing the boat. I have read other posts were people talked about staying overnight in Harwich - I'll try and dig-out some examples.