Marinating can definitely result in a wet surface, but it's fine as long as you pat-dry the surface of the steaks. Also, be sure to pre-heat the ProSear burner for at least 5 minutes before placing the steaks on the grill. These two steps should result in a better (and quicker) sear. When finished searing, leve the ProSear on high for about 5 minutes to burn off much of whatever may have dripped onto the surface of the ceramic plaque. Also use your shop-vac to vacuum the surface of the ProSear burner occasionally to remove surface debris that will inevitably fall on it. That ceramic plaque burner has hundreds or perhaps thousands of tiny holes in it through which the gas flows. If enough of them become clogged, it will not heat up properly.
OK, allow me to get a bit technical for a moment, and I would only probe more deeply into this if you suspect your grill isn't heating up properly...One thing to look for on a natural gas (NG) grill is the size of the input pipe coming out of the house. Often times, it is a 3/8" inside diameter pipe. That'll work fine for a basic NG grill but on a big grill like yours (which I'm guessing has a BTU rating of 75,000 or so), a 3/8" pipe could possibly starve the burners if they are all on at the same time which would prevent them from getting as hot as they are designed to. A 1/2" pipe would be better. If you are using only the ProSear burner, you should still be fine though. I should note that these pipe sizes assume you have the (more common) single-stage gas service having a water column pressure of 5-10.5 inches of water (i.e., 0.18 to 0.38 PSI). Some areas have a 2-stage input where the incoming PSI to the house goes from delivery pressure (~50 PSI) to 2 PSI in the first stage and from 2 PSI down to the range of 0.18 to 0.38 PSI in the 2nd stage. This configuration allows for the use of smaller diameter pipes thus supporting a higher BTU/hr at the outdoor appliance than a single stage setup. If a professional installed your grill, they should have hopefully taken the pipe diameter and inlet pressure into consideration.
Now back to grillin'. One other thing you could try is a reverse-sear. You would cook the meat slowly at a low temperature until the internal temperature is within 20°F or so of your target. Then, sear it. It will sear quicker since the surface of the meat is hotter than it would be going onto the grill just out of the fridge. Doing this will require a digital thermometer with a temperature probe during the slow-cook as well as a handheld digital thermometer to test the internal temperature after searing. The reverse sear works well for thick-cut steaks like tenderloin, ribeye, and NY strip. Remove the probe before you sear.
Yes, the Eye Round came out well. Searing and then low and slow cooking (around 200°F) take what is typically a lean, tough cut of meat and makes it much more tender. Doing this properly requires two temperature probes (or one 2-channel thermometer) - one for the meat and the other to monitor the temperature of the oven or grill. I did the slow cook in the oven and the oven temp can vary from the temperature shown on the knob or controls. Also, (and I hate to say it), but I wouldn't trust the built-in thermometer on your Lynx (or any other) grill either. If grill manufacturers wanted to cut costs a bit without jeopardizing the overall quality of the grill, they should discontinue putting those inaccurate analog thermometers on their grills. Even professionals on the BBQ circuit, with their expensive smokers, will use good digital thermometers to maintain their grill temps and monitor the internal temperature of the meat they are cooking.