Virtualization platform for older hardware (non Intel-VT/AMD-V)

Virtualbox? Most today take advantage of the extensions in order to give decent performance and features, as you've discovered.

The ultimate solution may be to spend $400 on a whitebox system to run an up to date hypervisor.

ESXi 3.5 still works. The first servers that incorporated the Intel VT extensions appeared in late 2005/ early 2006... Given the five major jumps in Intel CPU technology since then, your best bet is to try to find a modern low-cost system for your testing.

If you don't find something new, any used servers manufactured in the past 5-6 years would be compatible.