first of all sRGB is not the optimum color space for anything BUT the web. Adobe 1998 RGB is preferred right now, but even that is going to change with some new protocols. But sRGB is a very limited colorspace for web monitors.
next, you can't believe the monitor is calibrated. Either you do it every month or you don't. If you don't have a calibration device and run it every 30-60 days, there is no reason to go any further with color management and print making.
Everything you are doing in comparing the images on your monitor to how you want them to print is centered upon the calibration of a fixed color value of the monitor. You make the image look good on your monitor, but if the monitor colors are floating in space, your printer had no idea what you are trying to achieve.
You also need to shoot a color card in every series you shoot, and then you can batch correct the images from the same lighting set-up by adjusting the black, gray, and white swatches on the card to your monitor.
BUT, none of this means anything if the monitor is not calibrated and up to date. The monitor is the centerpiece of the whole deal because you are using that as your "judge" of correct color. Until you do the monitor, your prints are going to be trial and error. Color management is a difficult concept, but its the keystone of digital photography. You gotta learn the basics.
Also, why would set the printer to web graphics when you are printing? The destination source should be the type of paper you are printing on, and the color profile for the paper must be exact for each paper surface.