Should I be thinking about replacing some key engineered joists with lumber?
Believe me, I didn't make the purchase!
Nothing wrong with engineered lumber -in fact, it's often preferable to dimensional lumber because of the quality control it goes through.
The problem almost always stems from the engineer that does the specification on the floor system. Which, is often the builder's "guy" at the limber yard. The plans certainly have the floor system spelled out on them , but were tech followed , and was the design criteria sufficient?
A floor system that's adequate for hardwood may be insufficient for a tile floor and THAT floor may not be strong enough for when the "boss" falls in love with that marble just like the spa has.
It boils down to bending. The longer the span and more load (like stone tile , or pianos on the 3rd floor) - the stronger the joists need to be. This means taller joists and or shorter spans or both. When Jeremy says his floor flexes - undersized joists are probably the culprit. The subfloor is a small component of the assembly, and no wonder product subfloor is gonna make up for undersized joist. A poorly installed sub floor can be annoying which is why they are most often glued down in addition to nailed. The really attentive screw them down with glue, but most customers don't want to pay for that.
The blocking between the joists (or adding more) is going to do little to help Jeremy.
either. Rizzoas plan will work- it's called sistering, but it's no fun and is a real pain and $$$ if you have mechanicals running through the joist . I've never heard of it done on floors with engineered I-beams or web trusses, but I guess it's still doable.
You really need to take some measurements and then consult a span table to see what your dealing with to start. Then suggestions can be made for remedies. The other bad news is fixing most of theses kinds of things properly involves making a mess, so give up the "not making a mess" notion early on.