Hi Brian,
I would not invest a lot of time until you get some fruit off this
tree.
It's possibly an apple which you won't like. If height is a problem for
you, best to pull out what sounds like a full size tree, and replace it
with a dwarf, or at least a semi-dwarf tree. What you now have is a
tree with a large root structure that is trying to balance itself by
putting out abundant above ground growth.

Sherwin D.

Brian wrote:

I recently moved into a new house with what I believe is an apple tree. It
looks like the two major trunks were cut back at 7 foot a few years ago, but
since then a number of major branches have started from there and shot
straight up an additional 10 or more feet. I am reluctant to cut them off
because they are now a big part of the tree, but I certainly will not be
climbing that high to get the fruit!

I also don't want to get too radical in case I misidentified the tree...

Brian