Switch – 3-way chandelier switch strange behavior

I have a chandelier with 12x 100w incandescent bulbs and controlled by 2 3-way dimmers. I was going to replace the bulbs with LEDs, and I didn't think the dimmers were rated for LEDs, so I decided to just replace the dimmers with normal 3-way switches. The switches are rather near each other, so I checked that I knew what was going on with the continuity checker on my multi-meter. With the power off, I was able to find the two wires that ran directly from one switch to the other, and was sure to install them in the same location on each switch, and then of course with the hot on the remaining terminal of one switch, and the load on the remaining terminal of the other switch.

Now, everything basically seems like it's working… but every handful of times I turn the chandelier on (I can't find a pattern, and it seems to be with both switches), the lights only turn on very dimly (remember, these are not dimmers). If I fool with the switches (on/off a few times), then the lights turn all the way back on again.

Any ideas? I thought it might have been too much load for the switches (they are Leviton Preferred), so I took some of the lights out of the chandelier but it still does the same thing.

Any thoughts?

Update:
Ok, before I tested each switch separately, I noticed there is actually a Y from one of the traveler wires on both switches (the same one). After racking my brain, I actually found a THIRD switch that is connected to this light (this is a new house, sorry!)! So I guess this is a 4-way configuration? I also found little labels on the wires – I will write them below as:

'Label': function

Switch near door:
'5': hot/load
'3': Traveler A
'4' and '6': Traveler B

Switch near stairs:
'1': hot/load
'3': Traveler A
'2' and '4': Traveler B

Switch near kitchen:
'5', '6', and an unlabeled yellow wire (the ones with labels are all orange) – I don't know what these are function as.

I tried shorting the 3 'kitchen' wires together (as I don't even want this switch at all), but that made the other 2 behave oddly (in most positions of both switches the lights were on, but in the same 'dim' mode I was originally asking about). I also tried leaving the 3 'kitchen' wires disconnected entirely, but in that setup the light will not turn on at all with the other two switches.

Then I tried (with the 'kitchen' wires all disconnected) just setting it up as a normal 3-way switch (i.e. Disconnected '6' from 'door switch' and '2' from 'stairs switch'.), leaving me with:

Switch near door:
'5': hot/load (I guess? that's what I was assuming before the 4-way fiasco… '5' near 'kitchen switch' when disconnected shows current as well, so it seems like this is reasonable)
'3': Traveler A
'4': Traveler B

Switch near stairs:
'1': hot/load (I guess?)
'3': Traveler A
'4': Traveler B

However, in this case with my AC voltage detector all 6 wires read "live current", but the light does not turn on in any configuration of the two switches.

Any suggestions for next steps?

———- Update 2

You guys aren't going to believe this…
I went hunting around the house for the other end of wires '1' and '2' and found ANOTHER switch for this freaking light. (So what is this, a 5-way switch??). We'll call this one 'upstairs'.

Door:
'5'
'3'
'4' and '6'

Stairs:
'1'
'3'
'2' and '4'

Kitchen:
'5'
'6'
yellow

Upstairs:
'1'
'2'
red

So then each wire does the following:
'1' = stairs to upstairs
'2' = also stairs to upstairs
'3' = stairs to door
'4' = also stairs to door
'5' = kitchen to door
'6' = also kitchen to door
yellow = ? (perhaps to the light?)
red = ? (I think 'hot'?)

I'm out of time for tonight, but I guess I'm going to get power from another circuit in the 'kitchen' and try to turn on the light by connecting it to the yellow wire.