Experiencing occasional engine roughness at startup

Starting in the summer of 2018 I would experience occasional engine roughness at startup that would sometimes result in a check engine light. The roughness only lasted for a couple days, and the CEL was back off within a day or two. I mentioned it during my last two oil changes and the Ford dealer couldn’t find anything wrong. The first time, the error code came back to a crankcase pressure sensor, which was replaced under warranty. The next two times, the error codes came back to misfires on the number three cylinder. Now, with the CEL back on and roughness lasting for a week, Ford has decided that there must be a coolant leak inside the engine. They are bringing it in for a coolant system pressure test (after finding the coolant low) and planning on major work that will take the dealer a week to complete. They believe the roughness is related to coolant mixing with fuel in the cylinder, apparently a problem not unusual to the 1.5L. Something I feel like may be related, but Ford seemed like they had no idea what I was talking about, is possibly a fuel pump/primer issue. When you would step on the brake (but before pressing the start button) a pump could be heard in the rear of the car. That pump would run for about four seconds anytime the brake was stepped on prior to startup. This occurred always without noticeable exception. Around the time I started getting engine roughness at startup is when I noticed that the before-start pump wasn’t running like it used to. Occasionally it will run for the full four seconds but most of the time if it runs at all, it sounds staggered or intermittent. I just assumed the issue wasn’t coolant related and more of a fuel pump not priming the engine. Any ideas what’s going on?