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First… using the AC line neutral as a chassis ground is not permitted by the US electrical code, because it is possible for the neutral to have substantial AC voltage/current, which can damage whatever is connected to it that way, and pose a human safety hazard.
But regardless, the neutral becomes a part of the antenna system, and probably radiates at least as much as the 3-meter section above the tx (see paper 3 at http://rfry.org/Software%20&%20Misc%20Papers.htm ).
Even if you replace the neutral with an isolated wire leading from the tx chassis to a cold water pipe ground (or similar) — it also becomes part of the radiating antenna.
Installing buried radials somewhere near the antenna, and connecting the tx chassis to it again results in a radiating “ground lead.”
Using 3 or 4 symmetrically-arranged, horizontal radials laying across your attic floor would give you an RF ground plane for the 3-meter vertical to work against. Make them as (equally) long and straight as possible, solder them together where they converge below the tx, and connect the tx chassis to that common point. Remove any wire connecting the tx chassis to the AC neutral, or a separate wire to a water pipe ground.
This will change the feedpoint conditions at the antenna, so the loading coil settings will need to be checked and re-optimized.
The radials and any top hat used won’t change the vertical pattern of the antenna as long as they all are in the horizontal plane.
How an FCC inspector might view this installation with respect to the “3-meter rule” is a judgement call. The technical reality is that the top hat and radials are not contributing to the radiation of the ~3-meter vertical, but assuming that an FCC inspector might know that probably has some risk.