You could park a truck under there. Heck, you could park a truck under each individual joist if you wanted. If the truck ain't touching the bottom of the joist, then it's doing nothing to support the floor and reduce the deflection in the under-engineered system.
If you go down there w/ a stack of shims and a hammer to close up all the gaps, you're gonna wind up invariably moving the floor surface a little. If you've already put any thinset down to hold either your CBU or your tile, then you stand a good chance of inducing cracks and popping and crunching...
Hence the recommendation to get that all firmed up ahead of time.
(4x6 or 2x6 - either way sounds great. Bigger = better, definitely. Just gotta have it in contact w/ every one of the joists down there.)
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