Dawson, Chicken and Tok are the available places to fuel up. A fire last fall at the Boundary Roadhouse has them closed as far as I have heard. If anyone hears of them reopening, please let the rest of us know.
The ferry at Dawson tends to start running toward the end of May, just after the Yukon River ice goes out and they have the road plowed open. The Customs station is also seasonal so check as to when the plan to staff it and be open.
It has always been toward the second or third week of June or late fall when we have been over the Top. Several of our forum members have reported crossing in late May so hopefully one of them will post with better info than I have from personal experience.
Last trip I fueled in Dawson and the again in Tok. Was driving a Dodge then with a 34 gallon tank getting close to 15 mpg. Sounds like you would be fine to do the same. I think on the fuel stop sticky at the first of this section the miles between stations are listed. If not I have them on my web site.
If I was in the Dawson area at the end of May, I would plan on going over the Top unless local information advised not to do so. The Yukon DOT crews will have the best info or stop in and talk to the locally assigned law enforcement officers.
Did a quick check and it looks to be about 200 miles from Dawson to Tok with Chicken at about the half way point.