So variac noise depends on load, as you report, once your amp warms up it hums more.
Unfortunately, hum isn’t very predictable. Several transformers from the same lot may all be the same, or there may be one that hums less and one that hums more.
Your friend may be lucky. Or he may have an amp that has a much lower load than yours. or his electrical system may be better. A couple of things to try:
1. Take your humming variac to his house and plug his amp into it and see if it hums.
2. borrow his variac for an evening and see if his variac hums at your house.
One thing people chase with transformer hum is DC offset. I’m surprised someone hasn’t already suggested that. I have never found DC offset to be the problem. But there is always a first time so maybe that is your problem. DC offset can be caused by unbalanced loads on your home system, but not likely.
You might find that a larger variac/transformer hums less since it will be less loaded. OTOH, sometimes a larger transformer hums more regardless of load.
A variac allows you to dial in any voltage. this is handy in a lab but is not needed in your case. there are many fixed transformers available that convert from 120v to 100v. The ones on amazon are easy to return if they hum. I would oversize the transformer by at least 100%.
Jerry