One thing you can do is to pre-heat your LME before pouring it. This way it's already less viscous and will dissolve more readily. You should always be taking your wort off the heat before adding LME, because regardless of how fast you stir, the LME is going to dive right to the bottom- it is very dense. You should remove your wort from the heat, add your LME while stirring vigorously, and stir hard for a while before returning to the heat. That's probably your best bet for reducing caramelization, seeing as you're already doing late additions. Common practice is half at the beginning, half at the end.
I think you'll find the difference in hop utilization from wort gravity is pretty minimal. Of course, this is only true if your recipes are designed for a partial boil, not the other way round- you can only get so many isomerized alpha acids into solution. It's tough to get the big IBUs from a full boil recipe into a partial boil.
Moving to a full boil from a partial may net you a few IBUs more, but I don't think it's nearly as much as people say and I'm not sure I even trust the beer calculators on that one.
The one part of your post that gets me is this:
"simmer some hops and malt." Simmer is definitely not a thing we do in brewing.
You should start out steeping with 2.5-3 gallons at ~150 for 30-40min, bring to a boil, remove from heat, add half of your LME (mix THOROUGHLY), and return to boil.
Now your hop countdown starts (60, 20/15, 5/1 minute additions mean how many minutes left in the boil, or how long the hops get boiled, basically).
~10-15 minutes before the end of the boil, or with your second hop addition, remove from the heat again, and add/mix the rest of your LME. Return to a boil for the remaining time and remaining hop additions.
When your 60 minute boil is done, chill as fast as possible/top up to 5 gallons, aerate well, and pitch your yeast.