One other thing that might help, get an offset wrench. The handle has a 1 inch drop to the wrench's head, so it fits down into the opening. I don't know about your table, but most tables have a circular insert that fits into a large opening. You can change the size of opening to fit the bit by changing out the insert. In many cases, you must remove this to fit the wrench in to change the bit.
Another item. Drop a half inch grommet into the collet so the bit shaft rests on the grommet. You don't want the bit to bottom out in the collet, and this extra 1/8th inch of height will make it a little easier to get the wrench in there.
Some routers have a push button shaft lock, others require using two wrenches, one to keep the motor shaft from moving, the other to loosen/tighten the collet. If you have the button, you must reach under to depress this button when changing bits. That's in part why some here like their router attached to a plate they can lift out for bit changes and to set height.
Don't know about how your table works regarding inserts. The 16x32 inch one with green legs looks to have a very odd, diamond shaped dark area. Is that a removable insert? If not, you are up against a hard limit that will take the following action to deal with.
If you can't change the insert, I suggest you consider getting a table top with a mounting plate for the router--the easiest fix. Or you can adapt and/or create your own. Kreg has a plate that has a twist lock insert system that will solve your problem for about $70. You could probably adapt your table to fit it using your router and some guide rails made of 1x3 to guide your router in cutting the exact opening. You would add a second layer under the table (good ply will work. Cut a hole in this about half an inch smaller on each side of the opening than the size of the plate. You can add height adjustment screws to this to level the top of the plate with the top of the table.
Lay the plate on the top and center it. Draw a pencil outline and cut inside that line with a jig saw. Then lay out four pieces of wood right on the pencil lines (or fit to the edges of the plate with some playing cards to give you a tiny amount of wiggle room. Then you cut out the exact shape using about a 1 1/4 inch trim bit (with the bearing at the shaft end). The bearing rides on the four rails you clamped in place, and the cutters are set to cut just a mm or so deeper than the thickness of the plate. Voila, you have a really workable router table with all the modern features (although a little small) Later you can build your own talble using this same method, 2-layer top, exact opening for plate, a well cut 2x4 as a fence to start with.
You will need a 1 1/4 inch long, top bearing trim bit which generally comes with a 1/4 inch shank, which will require you use the 1/4 inch collet adapter. This bit goes for less than $25, and you'll find many uses for it in the future. That and roundover bits in the 1/4, 1/2 and 3/4 sizes, preferably with half inch shanks, which EVERYONE needs to make most projects look finished.
The experience of doing this will give you a considerable boost in confidence in using this most valued woodworking tool. It will be much easier to do than to describe.
Man, this got more detailed than I first intended, but having gone through exactly what you are just now, I figured it might save you some disappointments to go into detail now. The table mounted router is FAR SAFER than using it freehand, so you've already made that wise choice.
