Basement reinfocement

[sphelps]

Be warned that adding jack posts at random on a basement slab could do more harm than good. Typical basement support posts are placed on pre planned piles to minimize effects from ground expansion. Other areas in the basement don't offer such protection, in you put in a post and jam it tight any movement from the basement slab will transfer to the main floor. The seriousness of it depends on the soil conditions and the foundation but if you have cracks in your slab it's a good sign not to add such support posts.

Best option I think would be to add a beam from green post to green post if possible, however there must be support there already even if it's down the line further. So it's possible you're over thinking this, if your sub-floor is decent which it would be if it tile or hardwood then 135 gallons would probably be fine without concern. Perhaps relocating the sump would be a good idea to reduce the load but I really don't see a huge threat.