If you are thinking about scavenging an old electric upright bandsaw...just put a bigger electric motor on it. It would already be geared for the motors RPM. One big draw back is it would be a "ON or OFF" type deal instead of idle and a clutch to engage with rpm like a gas unless you could figure that part out. They make many electric bandsaw mills, I have never ran one. But one of the members here showed one his dad (?) has, and if I am not mistaken joasis has a buddy that runs one. Electric motor are actually more efficient for what you are talking, they make 2+ the torque as gas so a 3 hp electric would be more "powerful" that a 7 hp gas (if anyone knows the exact equation on that feel free to jump in) Plus no fumes it could be used in a shop.
The other things to consider are for one a larger blade, thicker and wider for a better cut. I think that would be a must. They would be available but the wheels on the machine may not accept them ?
The rolling down the track part would not be too difficult. A good solid base (deck) and the head suspended on a frame that has 4 wheels...
But having ran a sawmill I know that head is going to want to buck and jump cutting a hard log. It's going to want to pull the saw into the log. Let me explain that if I can. The torque you are applying to the blade/the friction of the cut pulls the sawmill head sideways, or if the log was not held securely just flip the log off the deck. There is alot of side force involved that you would not maybe understand until you had a chance to run a small bandmill. That racking force is where I said wood would not be my first choice, it is constantly under racking stress that I think would just tear it up unless it was made with great care (and a ton of wood and fasteners)
Raising and lowering the head for cut thickness is another challenge. For me probably the biggest challenge. You want that head to accurately raise and lower and stay there through the whole cut.
Those are the things off the tops of my head I see in design...I am sure there are 100 others. I am a big time tinkerer, but I don't think something like you are talking is something I would tackle. IMO unless you had access to a small warehouse of "odds and ends" you are going to end up spending more money that just buying an entry level mill like the Wood-Mizer LT10...it folds up out of the way when not in use