Laundry room remodel

Hello all I am in need of some advice. I am currently begining a remodel of the laundry room and need to relocate the washing machine. It is currently located on the wall opposite the dryer. I plan on moving it across the room to sit next to the dryer. Obviously I will need to rerun Hot/Cold water supply lines, but my problem is the drain. The current setup that is there for a drain now is not very good as it stands now. I had to concoct an elaborate setup just to allow the machine to drain and not overflow to the floor. The wall the machine sits against right now is a shared wall in what used to be an old garage. so the laundry room is on a cement slab and their is a raised foundation which the drain runs to the main line under the house. The problem seems to be this run from the laundry room to the main septic T is only 1"1/2 pipe and is at almost an incline to the T. I am guessing this is why I had to put a hose clamp on the washing machine drain line just so it wouldn't overflow the drain system?

So I guess what I am really asking is how is it possible to #1 replace the current long run with a 2" line and have the incline problem fixed. And #2 after this addressed, how do I need to run a drain system from across the room without going under the concrete slab? Any help or suggestions would be greatly appreaciated, Thanks. Matt.

Raise the floor up high enough to accommodate the new pipe size (2") and the amount of fall needed to prevent anymore problems. You will also need to vent this fixture. If it isn't vented this is half the reason for your problems.

The 2" washer drain must be trapped, vented, and have a 1/4" per foot slope to the main drainline.

drain

You are asking questions that require someone to see your installation in order to answer them. But in reality, a plumber is not going to come to your house, give you an estimate to do it, and then tell you how to do it so you can do it yourself.

The current drain system is vented and p trapped, so can I assume the slight incline instead of a decline to the main line is the reason for the improper draining of the washing machine?

Yes. Increase the size of the piping and give it proper slope.