I just looked back through this post to try to see exactly why you had the problem that you did, and then looked at Amazon for your model of Makita router to learn more about it.
For edging your projects I would have used the fixed base on the router and not the plunge base. I would also have made and installed an offset base to give me more router base surface, so it wouldn't be so easy to tip the router while doing the edging. Something like the base plate in this video, but I would prefer making it from clear Lexan so I could also see through it. The extra side handle helps you keep the router at 90 deg when doing the edging. You would hold this extended part of the base down and toward the center of your sign as you route the edge detail around all four edges of the sign to keep the router from tipping.
Another option for edging would be to use a router in a table. This would positively keep the router at 90 degrees to the work.
A plunge base with the plunge stops is great for routing the letters of your signs. You can even preset the stops for several different cutting depths. but a plunge base is not the best choice for trying to rout the sign edging, and the base on your router is so small that it's easy to tip the router as you try to rout the edges of your signs, causing it to dig in and ruin the edge. Since you have both bases, you should learn the benefits of both and use each where it will give you the best advantage. Also make or buy a bigger base plate for use with the fixed base when doing the edges.
I also made a larger oval base for the plunge base of my DWP611 that has extra handles (cabinet knobs) on the extremes of the oval base that I use when routing lettering in signs. Rockler sells a similar base #59811, but their's is a larger round base. The two handles make it easier to free hand guide the bit to follow the lines of the pattern.
Now, how about explaining in detail, maybe even with pictures, what is wrong with the plunge base of your DeWalt DWP611. Maybe I can help you fix it. Consider sending me a PM for this.