Will a snowblower get up a fairly steep long driveway?

you need to ask both the sales people and the maker's support pages for any particular brand you are considering.  Since the driveway is gravel, traction should be good [unless the weather produces ice on the ground -- lay in a 50 pound bag of rock salt at start of the season] and I've even seen chains on some snowblowers for added traction.  The worst hazard would be the machine falling back or over on YOU while it is running.  There's an inbuilt autonomic response in humans to hang on tightly when falling -- exactly the wrong response when using a snow blower.  -- grampa

We have a Honda 36” tracked unit an it handles steep grades. Super nice unit an can angle up to not dig into gravel. Our Honda 24” wheeled can do steep grades but struggles an takes some work. For the price of the tracked Honda you could buy a small used tractor tractor or atv with plow. 

It will handle whatever incline you can PUSH it up.

The problem you WILL have is that if you don't elevate the blades, you WILL be throwing gravel.

Fix the truck. At least get a tractor that you can ride.  You have a commercial grade need and using low end residential grade equipment will only cause you grief.

Frankly not a good replacement for the plow.  It's difficult to work one on gravel.  It will take you a LOT linger with a snow thrower.  But it can be done.