If you have the pulv, crovel or evis, you can bash as you engage zeds around a corner, which will allow you to slip past them. I find it to be more reliable and effective than trying to parry while running past and potentially getting knocked around.
Unfortunately you can't really be told how to carry properly. It requires experience, which means your team has to wipe lots before you can reliably carry with 50+ zeds left. Zerk with skirmisher is the perk to be for it, with firebug coming second due to fear and panic, or maybe medic for being able to heal yourself lots. When you're the last one left and scurrying around the map trying to survive, you'll often be cut off and killed really really quickly. Eventually you'll learn the safest routes to kite, and the most dangerous corners/stairs/doorways. There are some really unconventional routes I've started taking on Burning Paris which seem to be much safer than the ones I see people typically take. It's something that takes a lot of time to learn for each map, and requires a lot of wipes. I guess you could always try playing solo with some faked players. That might give you a feel for it.
By the way, it's unlikely to be due teleporting zeds, and more likely die to really close spawns. They spawn right around the corner, and even right behind you. I have videos of this that I might upload sometime, because it really needs to be fixed.