Drive to McCarthy,
It's not off road really, but many rental car agencies up here make you sign something saying that you will not take your rental vehicle on the McCarthy road (or the Denali HWY and Hall Rd). To get there you take the Edgerton HWY (30 miles south of Glennallen) to Chitna and the road starts there. It's about 60 miles in from Chitna. Once you get there you will actually have to park and walk the last mile to McCarthy (an old turn of the century mining town).
The Denali HWY is another good drive and it's in the same area, except north of Glennallen.
By the way, the AK state ferry doesn't go to Seward anymore (hasn't for about 2yrs.) It does stop in Whittier (It's the Kennicott and it will be going from Juneau to Whittier then Kodiak and finally Homer before turning around and making the reverse trip back to Juneau).
No idea on where the last gas station on the Haul road is, but I'm pretty sure you wouldn't have much trouble making it to the Arctic Circle.
Best advice I can give you is to get a copy of the Milepost. Even lifelong Alaskans use this publication.
Alaska Travel Guide and Alaska Trip Planner, The MILEPOST: Alaskan travel guide and Alaskan trip planner for Alaska, Yukon Territory, British Columbia, Alberta and Northwest Territories