Original Gravity too high for Saccharometer Scale

The only drawback would be the larger sample size required and that you need very accurate (i.e lab grade) mass and volumetric measurement. Your proposed method is sound, though. A hydrometer indicating 1.106SG means that your measured liquid has 1.106 times the density (i.e. mass per volume) of water. So weighing identical volumes of wort and water and comparing their mass (which has a 1:1 relationship to weight given that the Earth's gravity coefficient may be considered a constant here) will give you an accurate gravity reading.

Just keep in mind that most conversions between OG, Brix and Plato assume a middle-of-the-road gravity and may adjustments for very low or very high gravities (the latter being what you're dealing with).

That said, such an insane high OG won't necessarily give you a better beer. That's exactly the reason why hydrometers generally don't go that high. However, there are density meters that do, although they may not be intended for beer production. Mostimeters, for example, such as are used in wine production, max out at a lot more, but you'll probably need a conversion table to convert the mostimeter reading into OG. The Brix refractometer used in syrup production also go a lot higher. A typical syrup weighs in at around 70 degrees Brix which is equivalent to a specific gravity of 1.355.

However, the fact that you an raise your OG doesn't mean that you should, though. :-) The challenges of brewing a 15+% ABV beer are huge, from yeast stress, higher alcohol production and esters going through the roof, to the alcohol/body balance (read: you need a high final OG to balance out all that alcohol or it will be as rough as a bear's hind quarters). It can be done, and there are a few "Tyrannosaur" beers out there with 25% ABV or more (although one might wonder if these are technically still classifiable as beers) but be aware of the difficulties, and the chance of ending up with a beer that will kill a cow at a hundred paces. If this sort of brewing is your thing, go right ahead, of course! Just realize that it's not just a matter of simply pushing up your ABV.

Good luck!