Is there a limit (and if so, what is it) to the size (mass) of terrestrial planet that could be "captured" as a moon by a migrating gas giant?

I'm writing a novel where a colony ship crashes on such a moon. My research tells me that a moon around a gas-giant is not likely to be larger than 1:10,000th of the mass of its parent. If this is true, an Earth-like moon is unlikely to form around anything with less than 30 Jupiter masses, which puts the parent planet in the brown dwarf range. Not what I want.

So, can I get round this by having the gas giant migrate into the inner system, snaring a rocky world approximately the size of Earth, as it goes?

I'm not too concerned about other issues - I'm happy to fudge tidal locking, and have the gas giant only have a couple of other moons to avoid tidal heating, and stick the Earth-like moon 10ish million kms out to avoid the worst of the radiation. But I feel like I can't fudge the mass of the related bodies.

Any help, or related thoughts, would be greatly appreciated.

SOURCES: https://www.reddit.com/r/askscience/comments/32ixle/is_there_a_clear_maximum_gas_giant_moon_size/

This is indicative of similar sites and forums where I got the figures. I've struggled to find anything concrete anywhere else; language is vague, but supports the notion that there is a mass limit for moons forming around gas giants, and that an Earth-mass moon would require a gas giant of several multiples of Jupiter. One site I read suggested that Earth-sized ice moons might form past 10 Jupiter masses, but that any terrestrial moon would be considerably smaller. Obviously, I'm looking for an Earth-mass, terrestrial planet, not a slushie world, and I want to avoid small terrestrial worlds because of the low-gravity.

I'm grateful for the response re the Roche Limit. I did wonder about two planets orbiting a mutual gravitational center, but I don't know how to figure out what kind of effects that might have on the Earth-like planet, and whether I could keep it far enough outside the gas giant's radiation belts.

Thanks for all the replies so far.