If you want to keep the tree and don't mind the tree being against the roof like that, then the gutter could be installed all the way except for the tree location, and right above the tree you could install a rain diverter under the lowest shingles to deflect the rain into the gutter at that end.

Your right about topping, it can lead to wood rot and disease starting at the large cuts, and if enough is removed, it can shock the tree and even kill it.

in my world .. warped as it is..

there is no upside to that tree .....

kill it... i dont care if you hate that ... .. cut it to about 3 feet.. and start digging.... and use the 3 feet to wiggle it around.. as you excavate ..... [make sure there are no utilities below]

and then plant something appropriate.. so it wont grow in the gutters..

this tree.. ought to have been.. properly planted.. at LEAST 20 feet from the house ... and that is the base problem ... so dispose of the problem ...

and if you are feeling guilty.. plant 2 or 3 more trees to offset the lose of this piece of carp ...

to clarify .. lol ... you are putting your hundred thou house at risk .. for what is most likely.. an invasive pear.. ... improperly planted.. two freakin feet from your castle ....

the nimrod who planted a 40 to 60 foot tree... that far from the house.. ought to have his shovel taken away ...

i hope you have a sense of humor...

KILL IT .. REMOVE IT.. AND BE DONE WITH IT ....

ken

ps: i would suggest castrating him with his dull shovel also ... but i wont say that aloud ....

Tree is already badly over-pruned (stripped) and cannot remain in that spot with or without being additionally brutalized - there is no room for it so close to the house. Cut it down and keep it regularly cut off until the stump wears out and quits sprouting.

I'll join the chorus and say take it down and out any way you choose. It looks as if the garage is detached from the house. Doesn't matter. Get rid of it for all the reasons stated above.
Pear makes good firewood!
Mike

I just feel I am in a Roman gladiators arena and every body is pointing his thumb down ,kill it ,kill it ,kill it !

Thumb down!

Just for conversation because this will sign you up for yearly pruning work until the replacement is ready.

If this tree produces decent pears you like...

Is there any possibility of cutting both them awful branches back to thebmain trunk and letting the tree resprout for the sake of getting fruit for the next couple years until whatever you plant to replace it is ready?

It will never look American natural that way and will be tons of work. Bet you loose this years flowers and fruit. It would just be a thing to experiment with.