IANAL, but, if you have an LTC-A that sporting restriction applies to where you can carry concealed outside of your home. Assuming the homeowner for whom you are housesitting has no problem with you bringing guns inside the home you should not have an issue. You will have to transport any guns according to MGL.
Nothing prohibits it, providing it is "carried by or under the control of the owner or other lawfully authorized user", or properly "secured" (M.G.L. c.140 s.131L(a)).
When on guard, in the house, jus' remember, you need to be wearing the shotgun in your holster and on your bod or else it needs to be locked up or have a trigger guard. Now, "Right shoulder, arms!"