laundry machine backup soap suds into laundry tub.

I have the drain and trap in for my basement bathtub and have poured cement over most of my plumbing with the exception of a small boxout arround the Tubs U-Bend.

Today, I was doing laundry and I got a small amount of soap suds coming up the pipe for where the tub is supposed to go in.

I was thinking if of attaching 1+1/2 in backwater valve vertically between the trap and the tubs drain T.

But I'm worried about:
A) I won't have enough room (without raising the tub an inch or so).
B) the valve won't work with suds.
C) it will slow the tub draining time.

So I'm looking for advice and suggestions.

Thanks.