Puzzled over a trunk that wont work unless it's running on a 100Mb/s interface

I know what you're probably thinking - but hear me out.

Recently, a vendor ran two CAT6 links from an IDF inside the org (CAT5e patch panel) to a terminal outside the building to support network connectivity for a temporary structure we've put up.

I installed a 3750 (48x FE copper, x4 GE SFP) in the structure and configured it to trunk with a 6500 chassis which sits inside the IDF. When it came time to plug everything in, I found that the interfaces which were supposed to be trunking were actually in a notconnect state. The configs are super simple - no VLAN pruning or native VLAN bullshit. Just "switchport mode trunk" on both sides. So, I started looking at the hardware.

I swapped SFPs (tried multiple GLC-TE and GLC-T copper SFPs), tried multiple GE interfaces on the 3750 and 6500, swapped cables (CAT5e and CAT6), verified speed/duplex settings, etc. Nothing worked.

I finally yanked the trunk link from the GE interface of the 3750 and slapped it into a FE interface - and behold, it worked! Trunk was up, phones started registering, etc.

For the sake of troubleshooting, I swapped out the 3750 for a brand new 9300 and tried again. No dice. The trunk simply won't come up on a 1Gb interface.

I need the 1Gb uplink to support some bandwidth-hungry equipment which will sit in the temporary structure. I only have two copper lines, so the best I can do with a port channel is 200Mb/s on the 3750.

The vendor claims that they used CAT6 cables all the way through and terminated on a CAT5e patch panel in our IDF. I assume , but do not know, that the temporary structure (which was brought to us by a vendor and already has some cabling infrastructure) uses CAT5e at least, since they have their own gigabit switches which they offered to provide for us.

I'm at a loss at this point. How else could this be broken for 1Gb connections, but not 100Mb connections?