Solution was easy and cost me $10: buy a used T7250 on e-bay and plug it in. Not only it supports virtualization, but it is also noticeably faster.
Replacement takes 5 minutes
It is really worth noting here, how inexpensive developer-grade hardware could be these days.
There were reports of more powerful upgrades possible for that laptop (T8000 and T9000 series). Nevertheless, the T7250 seems like an excellent value for money to me. You get faster laptop and virtualization support for ten bucks - that's unbeatable.