Here is once again the kernel of the argument, why you and I see it differently.

Inertial-mass is always equivalent to its gravitational-mass. Let me illustrated it thus:

Take a one kilogram mass (same cube or rod or ball or whatever, did not change its composition in any way) from Earth's 1 G and move it to Jupiter's (hypo) 5 G. Place this kilogram of mass on a balance scale, and it balances against another kilogram mass. Now try lifting this kilogram off Jupiter's surface: it will take 5 times the force to do so. I interpret this as 5F = 5m*a; while you interpret this as 5F = m*5a; this is our fundamental difference. But Jupiter is not 5 times the mass it was before, same mass. If Jupiter were 5 times larger mass, than we operate in 1G, where 5F = m* 5a; but if Jupiter is still the same mass, we operate in 5G, where 5F = 5m*a, which means Jupiter's "kilogram" is one-fifth Earth's kilogram.. Now take a one "kilogram" mass from Jupiter, which is one-fifth the size of our previous mass, and take it to Earth's 1 G. Place that 0.2 mass on a balance scale with Earth's one kilogram mass, and the Earthian kilogram wins hands down. This is why Jupiter (if it really is in 5 G) is a far smaller planet core than we realize. Because this core is hidden by its incredibly vast atmosphere, we can't see it, though Voyager reported that it is about two or three Earth masses, which is still very small. Yet Jupiter's small core is operating in 5 G, so it balances on a scale with Earth 1 G mass, but it would take ten to fifteen Earths to do so. If you tried to move 10 to 15 Earths rather than two to three Earths, you would need a great deal more force, and that is why the inertial mass and gravitational mass are equivalent.

Here is something by way of illustration that maybe will give you a better sense of what I am talking about: Enceladus, especially where they say:

"Likewise, with the atmosphere, Enceladus does not possess the gravitational attraction necessary to hold on to a cloud of water ions, so this must be being replenished also."

Only problem, Enceladus being about the size of Arizona, is too small gravitationally in 1 G; but it may not be too small in 5-10 G (I think Saturn has ~10 G). The scientists who are puzzling over this (they know nothing of a greater G) are saying that there must be a source replenishing these water ions, and atmosphere. But there is no evidence of this since we began looking, so they're mystified, naturally.

This is why mass behaves differently in 1 G or 5 G: in 5 G it can do things that in 1 G it cannot, like hold onto more ambient mass, gases, water ions, etc. BTW, the current thought is that Saturn's core planet must be much larger than Jupiter's small core, but that again is a function of not knowing that G on Saturn may be twice that of Jupiter, so to compensate theory they give Saturn a bigger core, which has not been found to date due to Saturn's thicker (bigger G, hypothetically) atmosphere.

I think where you run into trouble here, conceptually (and why this whole idea rubs you the wrong way), is that by referring back to all our spaceprobes that successfully maneuvered their way around Jupiter and Saturn, there was no variable G ever detected. And this is positively true, but we may have the planet's mass-volume figured in 1 G, when it fact it should be substantially smaller in 5 G. We use gravity assist, which is a function of (G*m) to navigate the spacecrafts, and the spacecraft mass is infinitesimal in comparison to the mass of the planet, so everything more or less works fine (after a few inflight adjustments). You see, it is well hidden, even if wrong, because we modeled the universe after our planet's 1 G environment, so even if the G is different elsewhere, we can't tell... well, except for all the puzzling things like an atmosphere on Enceladus or Pluto, where we explain it away saying that they are "gassing out". End result? We get a very confused view of cosmological events from our solar system out to deep space. Is the Pioneers Anomaly giving us a clue? Most people, including yourself, don't think any of these puzzling phenomena are gravitational. I do...* But I do not wish to convince, only to illustrate how I see it, and remember I may be wrong.

*(I think it is at least possible, but we can't know until we find a way to measure for this, so only hypothetical for now.)

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