Doesn't it bother you that a present perfect tense in an
if clause is used with
would?
Isn't the past usually used with would in that case?
It is unusual. The reason it's OK is that would like to (or would love to) is an idiom equivalent to want to (a present tense). 
So it's like
I hope you've seen it, but if you haven't, I'd love to run it for you now. ~
I hope you've seen it, but if you haven't, I want to run it for you now.
CJ