I’ve never seen a GeForce 2+ card that doesn’t work with an out-of-spec AGP bus speed. There might be some cheapo models out there with this issue, though…
I’ve successfully tested A LOT of cards such as GeForce 2 GTS/Pro/Ti, GeForce 3 (Ti200/500), GeForce 4 Mx440/460 and GeForce 4Ti 4200/4400/4600 on 440BX motherboards running at FSB133, and never have I had an issue that was caused specifically by the video card. The issues are usually related to the motherboard itself (some fail to run properly at FSB133, but work very well at FSB124), or some other peripheral.
Based on your tests, it does seem (at first) that the video card is to blame, but it’s still not 100% conclusive. I would do some more tests with the bare minimum (just the motherboard, CPU, RAM, video card, HDD) on a fresh installation wih driver version 30.82 (one of the fastest and most stable for GeForce 4 MX/Ti cards).
2 x PGA132 / 5 x Socket 3 / 4 x Socket 7 / 6 x Super Socket 7 / 5 x Slot 1 / 3 x Slot A
5 x Socket 370 / 5 x Socket A / 1 x Socket 478 / 2 x Socket 754 / 3 x Socket 939 / 4 x LGA775 / 1 x LGA1155
Current rig: Ryzen 5 3600X
Backup rig: Core i7 7700k