When multiplying psi with in^3, the resulting answer is defaulting to length^2*mass/time^2 rather than lb*in. How can this be changed?

"Tools", "worksheet Options", "Dimensions" tab, uncheck "Display dimensions".

You can type the units you desire:

And Mathcad will adjust the value to match.  note that psi is pounds force per square inch, the unit lb is pounds mass, not pounds force (which is "lbf")