Can a foreign national living in the US drive on a foreign license outside their home state?

My advice is to invest the time and exchange your license to avoid unnecessary problems.

There are so many different regulations, state by state, that the chances of falling faul with one of them are high.

There is also the problem that the Police may not know how to deal with Foreign License properly.

There is also another aspect that should not be ignored: as a Maryland resident not having a Maryland license may be considered for the Police as strange and suspect you (as a foreigner) of some something far worse than just not having a valid license.

Last but not least: at some point your license will expire and since most jurisdictions will not renew a license of a non-resident you will have no license at all and must start again from scratch.

A exchanged license will retain the information of the original issuer.
When returning to you home country the Maryland license can be exchanged back.

USAGov site: Foreign Nationals Driving in the U.S. states:

Residents (Non-U.S. Citizens) The residency requirement for obtaining a U.S. driver's license is different in each state:

• If you are eligible to apply for a driver's license, you must get a driver's license from the state where you live.
• Check the requirements and find out how to apply in your state's department of motor vehicles.
• A U.S. driver's license allows you to drive anywhere in the U.S. It is your responsibility to know and obey the laws of the state where you are driving.

Since you are eligible the first statement applies to you. The last point also makes it clear how complex the matter can become.

A Lawyers site warns about possible problems with the Police not knowing how to deal with foreign licenses:

Generally speaking, if you are NOT a Maryland resident and you have a valid international license from your country of origin, its OK to drive with that license. Unfortunately, individuals with a valid international license who drive in Maryland often get charged with driving without a license. Driving without a license is a serious Maryland traffic offense, which carries jail time. I see these Maryland traffic cases all the time. I believe police officers simply don’t know that its permissible to drive with these licenses, they don’t believe the licenses are authentic, OR they belive that the individual is actually a resident of Maryland. If you are a resident of Maryland, the law is not clear on how long you have to obtain a Maryland license. If you have an out of state (not out of the country license) and you become a resident of Maryland, you have 60 days to obtain a Maryland license.

Pennsylvania warns, as one state regulation of many, of a time limit since arrival in the United States:

5. Can I drive in Pennsylvania with my Foreign Driver's License?
   Individuals who possess a valid foreign driver's license from their country are authorized to drive in Pennsylvania for up to one year from their date of entry into the United States, or upon expiration of their foreign license, whichever comes first. International driving permits are strongly recommended, but not required.

This case shows that, for Pennsylvania, you may not drive at all since you have been in the United States longer than a year.

As far as I can tell from the California site, such a time restriction does not exist.

Colorado Driver’s License Requirements for Visiting Foreigners

Foreign visitors driving requirements pertain to any non-permanent resident with an international driver license or a driver’s license from another country who plans on driving in Colorado for longer than 90 days.

This point does not apply to you for 2 reasons

• you will be there less than 90 days
• you are a permanent resident (not a visitor to the United States)

I didn't see the combination of permanent resident and foreign license...

And these are only 3 of the 49 mainland jurisdictions of the US.