Heavy or lightweight flywheel?

With a starter gear of 12.18 taking off should not be a problem.
In your case, at 1000 rpm your minimum roadspeed is around 6.5 mph, so again, you don't need a heavy FW.
So all-in-all, with the new information I see no reason to run a heavy FW.
Butum, I still would.

I have never seen a ring gear come loose period, unless it cracks. When the RG is installed, it is first heated very hot to expand it, then quickly dropped onto the FW which was earlier set up to accept it, in such a manner that when it drops on, it is in it's final resting place. As it cools it shrinks on. I can't recall ever seeing a Mopar FW with a welded-on RG.
After installation, there is nothing you can do to the FW that would make it fall off, unless it cracked.
So, IMO, if a RG comes loose, that is defective. Either the RG was sized wrong or it has cracked.
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But I'm curious why your engine needs to idle at 1000. Just how big a cam are you running, and at what Dcr or cylinder pressure and what idle-timing.
The biggest cam I have tuned is the 292/292/108; and while there is no denying that it has a personality, I have got them fairly stable at 750.
But yeah, I had to adjust my TTIs to not rattle on things.