If you're going to cut it and have approval from the landlord and all that, i think your plan to dig around it will work. Also consider using a hose/pressure washer to clean rocks and dirt off the root before you cut it to minimize the damage to your cutting tool of choice..
what they said.. how big is the root diameter? here many arborist prune lilac and such with sawzaa they sell 8 and 12 inch blades for tree cutting.. look around your stores.. IMO a 6 dollar sawzaa blade is easier to replace than a bar and chain.. many homeowners that live on small property use sawzaa instead of chainsaw for branches and such because they are more cofortable with it
I have used my diamond blade cut off saw. You could also slab off 1/2 of the top, seal and cover with your choice of material.
Get a pruning blade a sawzall will cut it pretty quick . Diablo 9 in. 5 Teeth per in. Fleam Ground-Pruning Reciprocating Saw Blade (5-Pack)-DS0905FG5 - The Home Depot 9 in. 4-5 TPI Reciprocating Saw Pruning Blades 5 Pc
I'd bring in a load of 1" pea stone myself and raise the grade about 6 inches. . Can be Nice to walk on when it's raining. That root looks like it was cut to dig the foundation a long time ago. Probably five or six roots spanned out around the foundation where it was cut. That tree is kinda close to the house too. Some would remove the whole tree around here.
