One-part self-curing putties are the best for filling these types of gaps/panel lines/gridwork, IMO. Agreed Perfesser, an epoxy putty is not well suited to that particular sort of filling on broad surfaces. Once again, I advocate strongly for using plastic sheet, strip, or other shapes (as necessary) for filling gaps, rather than putty, to ensure that as much of my model remains plastic as possible. If I'm not making large mods to my build, minimal puttying is best; gluing in plastic is ideal. Troweling on loads of solvent-filled putty will sometimes deform the plastic if it's thin, and creates extra work when sanding down to your final surface. And what if you go too far? MORE putty?? Luckily the 1/537 plastic is approximately .060" in most areas, so you actually can heap on putty without real fear of harming the kit, just don't breathe too deep...I had similar experience with it. Went and grabbed the two containers of it last used a couple of months ago and both were hard or partially hardened. Tossed 'em both.
Going back to bondo for the times I need such a thing. If it's just a small area, I use epoxy putty but it's not very friendly for doing large scale filling-in of grid lines.
On the 1/537 panel lines, Bondo, spot glazing putty, Tamiya white polyester, (Squadron and Testors shrink too much for my taste) or anything similar would be the way I would go, and have done so before. I do however want to give the liquid goo angle a trial on one or two of the kit parts to see what exactly the technique would be. I have a feeling it's not as simple as it sounds...