Talk about lazy.naw, I located a plumbing supply house that has the same fitting and I'm going to do it my way. build a base and have it slope over and run into the same pipe thats there now.
I could have changed out your p-trap and relocated in one hour.
And it would work better, it would be code and suprise surprise, when your wife's long hair starts clogging the drain, you will be able to run a snake down it to clear it.
All you're doing is ensuring problems later for yourself, and you will spend more time doing it wrong, and with more parts, then a plumber, or all the rest of the DIY here could have done it in.
It's so simple to do this right, that it just amazes me that you "think" you are saving money somehow.
This is a joke,
Right, you don't really intend to do this.
You are spending way too much time trying to find a harder way to do this.
Just for fun, try pushing a snake through those fittings. If the snake won't go through now, it isn't going to be any better later.