I'm Looking for a phrase that means putting your back or muscle into a task, like rowing.
Is there another word for "it", as in "put your back into it"---is there another way to say it, such as "leaning into..."
"Put your back into it" is an idiom, so you wouldn't phrase it otherwise, and it does not necessarily have to be applied to physical labor. If you don't want to use that phrase, you need to come up with another idiom or just use a description of what's happening. So you might say that "the Oxford crew clutched their oars and pulled with all their strength, but they couldn't match the sheer muscle power of the Cambridge oarsmen."
Back-breaking work is often used to describe physical labouring jobs and sometimes other events.
In the UK people say Give it some wellie. It wouldn't be used in a formal situation.
- To increase fuel or power to an engine, as to a car by depressing the accelerator (gas pedal).
- To apply great physical effort to (something)
Another idiom used to mean putting more effort into something is the admonition to put some elbow grease into it. This phrase is primarily used in connection with manual labor and would not fit as well with an activity like rowing.
Elbow grease is an idiom for working hard at manual labour, as in "You need to use some elbow grease." It is a humorous reflection of the fact that some tasks can only be achieved by hard effort and human energy, contrasting with the idea that there should be some special oil, tool or chemical product to make the job easier.
More on the history of the phrase can be found here on ELU:
You might be looking for "to bend one's back".
E.g.: The bowlers need to bend their backs to exact bounce from this wicket.