RJ11 is a 4-conductor spec. RJ45 is 8-conductor. Perhaps you're thinking of RJ12, which is 6-conductor. I have seen a number of contractors use RJ45 jacks for RJ12 termination, I suppose just to make things simpler, but that doesn't solve your problem.

Certainly the common ethernet specs use pins 1,2,3 and 6 on an RJ45 cable, but I don't know where you get that RJ12 does the same for phones. IIRC, and I may not, it uses 3 and 4 for line 1 and 2 and 5 for line 2. I assume that it uses 1 and 6 for line 3, but I don't know that at all. However, even if I'm wrong and RJ12 uses pins 1,2,3 and 6, they wouldn't be the same as pins 1,2,3 and 6 on RJ45, They'd be the same as pins 2,3,4 and 7. Remember that the RJ12 connectors are going to be set one in on either side from RJ45.

That being said, the center pair in ethernet applications is unused and IIRC that the center pair is line 1 for phones, then you could conceivably wire both phones and ethernet to the same jack. Of course, you'd only be able to use one at a time without an adapter of some nature, and I have no idea if the voltage over the center pair might damage your NIC or computer.

The real thing is that you're going to have to rewire it anyway in order to get any ethernet, as Tony pointed out. Why not go ahead and do it right?

If you know where the wires are running to, you might be able to pull them through the walls and attach a nylon string to them as you do. You could then use that to guide a fish tape through the walls to pull real cabling.