Four way switch wiring
In a very similar situation, I turned off the power and disconnected all the switches and in a logical sequence using a volt-ohm meter (or toner and receiver) I determined which box had the hot lead, which were just travelers (usually the one with two reds) and which connected to the light. I drew an image of the results and the diagram makes it much easier to ‘picture’ your circuits. You realize that a single red is the beginning or ending traveler connected to the four-way in the middle. Be aware that when you see another black-white in the same box it is likely another circuit not related to your four-way. You can use a three-way at the ends but only a four-way in the middle where the two reds are located. Of course it can be much more complicated if you have two separate four-ways in the same box or if the light is not at the end of the circuit but in the middle or beginning (where the ‘hot’ lead is found). That may be when you need to employ a real-live electrician.