For transformers with two secondaries load *BOTH* secondaries! If you don't, the losses in the primary are far lower, and its impossible to calculate the true equivalent resistance referred to the secondary.
You aren't going to damage the transformers running them at 100% load for 10 minutes in free air. In fact they'd probably be OK with 150% load (50% overload) for that long starting from cold as there is a fair bit of thermal mass so no part of the winding is likely to exceed its maximum insulation temperature. Its therefore good practice to aim for 80%-100% of full load when testing.
For the 50VA transformer please use 2x 20W bulbs, one on each secondary, as 20VA@12V is 1.67A RMS which, when you apply a factor of 0.62 for bridge rectification with capacitive input load, corresponds to a DC load current of 1A, which is right where we want to be operating as max load for a LM317/LM337 based PSU.
Normally you'd load the 100VA transformer with 2x 20W bulbs PER SECONDARY, but as you specifically are using regulators with a max rating of 1.5A DC, there is no point in going over 2.4A RMS which is 30W @12V.
Due to the non-linear resistance vs voltage curve of the bulbs, it would also be helpful if you measured the actual load current of one of the bulbs for each transformer.
Also, for our convenience and to guard against mains voltage fluctuations with time of day or week, please repeat the unloaded voltage measurements immediately before and after the loaded measurements and post all the results in the same post.
So far it looks like the 100VA transformer is likely to be the best bet.
Turning on your heater or air-conditioner etc. is unlikely to have much effect unless your house's wiring is in particularly poor condition. Problems start when a high proportion of the population turn on a high load appliance at the same time. The classic case was the U.K's Coronation Street soap opera on ITV, which regularily aired late afternoon. During its commercial breaks, you could bet that a high proportion of its viewers (over 9 million households in the '60's and '70's) would turn on a 3KW kettle.
https://en.wikipedia.org/wiki/TV_pickupDinorweg pumped storage powerstation in the UK was built to time-shift peak loads, but as it has the fastest spin-up time for a major power station in the UK, its currently mostly used to supply the rapid demand surges caused caused by TV pickup.
https://en.wikipedia.org/wiki/Dinorwig_Power_Station(Its pretty incredible - 12 seconds to go from near 0 to 1320 MW)