Robert,
Sounds like you have it narrowed down. Gas Jet seems most likely to me as well.
Don't give up! The K-4 is a very agile and strong engine...I was able to walk off with 24 loaded MDC hoppers (10 lbs a piece) with nary a hitch or slip of the driver. The major thing to remember is to always keep the water glass full! These boilers had the glass mounted 1/4" lower than they should have, so all readings are 1/4" off on the glass. Replacing a boiler is not the funnest task, either. Other than that, they are very good engines, docile and easy to operate.
Leaks can be sealed up fairly easily. In the interim of waiting for parts from Hans, maybe focus on getting the tender leak-free? As for the side-side issue, I have a solition for you. Get some colt .45 caliber pistol firing pin springs, disassemble the truck and cut the firing pin springs to length, then replace two of the OEM springs with the new firing pin springs, be sure to stagger them diagonaly across from one another. This stiffens up the tender trucks and helps prevent the side-side rocking, not to mention the dreaded rear end sag that occurs as the springs age, causing the coupler to drop down.
You can contact me off list (TR3services/at/gmail.com) if you become truly stuck. Always glad to help.