The only way in which you could safely use any modern PSU with a Barton 3000+, would be to find a motherboard with the 12V CPU power connector.
Unfortunately, I've never had a VIA KT600/880 motherboard with this connector. Apparently there are some out there, but they're probably rare. Furthermore, for a time machine PC, I would avoid the KT880 motherboards anyway, because their BIOS seems to lack certain features (like disabling both the L1 and L2 cache). KT400 or older are not good, since your CPU needs a 400MHz FSB - so that leaves us with KT600. Good luck finding one with the CPU power connector. 😀
If you give up the idea of building a time machine PC with DOS capabilities, then you can take into account an nForce 2 Ultra board (and many of those do have the CPU connector).
Personally, I can recommend the Thermaltake TR2-470W PSU. It has a combined 3.3V+5V max wattage of 220W and can handle anything up to a Barton 3200+ without any issues.
EDIT: Your PSU has a max combined wattage of 700+W for all rails. The 3.3V and 5V rails are probably DC-DC converted from 12V. Also, the 3.3V and 5V are pretty solid with 25Amps each, so there's a chance it might work OK (if those values are real, I'm not very familiar with Raidmax PSUs). You'll just have to test, but remember to monitor the voltages. If you see the 5V rail drop below 4.8V, that's a good sign that the PSU can't handle the current.
4 x Socket 3 / 3 x Socket 7 / 4 x Super Socket 7 / 4 x Slot 1 / 2 x Slot A / 5 x Socket 370
3 x Socket A / 1 x Socket 478 / 2 x Socket 754 / 3 x Socket 939 / 2 x LGA775 / 1 x LGA1155
Current rig: AM4 - Ryzen 5 3600X
Backup rig: LGA1151 - Core i7 7700k