What deflection calc are you using?..
I think your over thinking this and deflection is quiet complicated and with out knowing span tables face grain which engineeres are the ones who can really figure out and put it in English.

You have 16" oc joist what are the size are the joists and how many Colums do you have under neith the kitchen tht hold up the joists.

I'm using the online deflectometer available at a popular tiling website. I seem to see many refer to this meter for determining span deflection.

The joists are 2X10 Douglas fir boards resting on the basement walls and the other end on a steel i-beam that goes beneath the room to be tiled. One side of the room has a 8' span to the i-beam, the other is 15.5'. The large i-beam has several columns supporting it.

I'm no engineer so I appreciate whatever advice can be given. I usually try to overbuild in my projects to minimize the possibility of miscalculation leading to problems.

Yes one side is the sill plate, then you have your i beam from one side of the house to the other that is held up by lolly colums then your joists that run off the i beam.

You will be fine if you just add ply.

Thanks JetSwet. Based on some other posts I have now read, a good alternative to the lally columns seems to be to build shelving at the critical point. I need some utility shelving in the basement anyway.
When you say 'add ply,' I assume you mean to the top of the floor to increase the subfloor thickness to 1 1/4" ? Or were you referring to the underside? I see some have posted adding ply to the underside of a floor to avoid building it too high. Is this as simple as cutting out 3/4" exterior plywood to fit snugly between joists, glueing it to the underside and adding cleats to hold it in place? Does this add significant stiffness?

Blocking underneath and additional plywood on the surface would probably be enough.

Another option would be to sister the joists. Plug in 4x10 to the deflectolator and you'll see that you've got sufficient support.

I wouldn't do the plywood.

You can sister, cats, cross blocking all you want, you will still have bounce with with in the plywood. Adding anoth layer of ply....seams offset will deflect the bounce.