My main fishing lake is small and loaded with vegetation. Are square bills effective running on top of the submerged grass like the old rattle traps?

Depends on the squarebill and how much water you have.  A lot of squarebills are 3-5’ divers so if you’re running across the top of submerged grass that is 1’ under the surface it won’t work.  You’ll need more of a baby 1 minus or wake crank type bait.  Or a rattletrap.  

Sure. The issue is how much of a water column do you have?  You will want a bait that runs the optimal depth or a bait you can manipulate by stop and go retrieves to give the bait time to float up. Balsa is good for that.  Ticking tops and ripping free can be productive.  Some baits that shine are the SK Head Hunter, 6th Sense Munch or Curve 55 Finesse and the Man’s Baby 1 Minus.  Have fun.

I've had success cranking a squarebill with a sweep/reel or burn/stop even when it isn't banging against stuff. I've not fished it specifically over submerged grass.

As everyone else has said, it all depends on the depth of the grass.
 

I usually use a lipless along the grass lines, but in shallow stuff I like to toss an extra shallow crank like a Bagley Wake or a Fat John 50.

14 hours ago, LokiDawg said:

My main fishing lake is small and loaded with vegetation.

How far below the surface are the weeds in your preferred locations?

I’m using a fluke or a trigged bait of some sort.. 

2 hours ago, PhishLI said:

How far below the surface are the weeds in your preferred locations?

Around the bank is emergent. At the edge of the emergent vegetation the submerged vegetation starts out at 2ft below the surface then drops down quickly to 8-12 feet below the surface. And it's basically like that around the whole lake

Next question: Are you fishing off the bank or floating? 
 

If fishing off a boat/kayak/inner tube, it might be advantageous to throw a shallow diver toward the bank and pull it toward you - something like a Big O that won’t bottom out but will follow the transition downward. If fishing it from the bank, you’re kind of limited to the top of the column (unless you like snagging constantly).

1 hour ago, LokiDawg said:

Around the bank is emergent. At the edge of the emergent vegetation the submerged vegetation starts out at 2ft below the surface

For this zone take a hard look at the Livingston Bullnose 70mm wake. Depending on your retrieve speed, it'll crank down to about 1'-2' below the surface, and is essentially silent. This bait comes through emergent weeds remarkably well, especially if you fish it with a 15lb fluoro leader, or mainline, which will slightly pull the nose down which hides the front treble behind its bill. It's been a killer for me when they're feeding up over high grass and are uninterested in baits that are more chaotic. Rattles, pops, plops, etc.

 

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Bull Nose – Livingston Lures

 

4 hours ago, ElGuapo928 said:

Next question: Are you fishing off the bank or floating? 
 

If fishing off a boat/kayak/inner tube, it might be advantageous to throw a shallow diver toward the bank and pull it toward you - something like a Big O that won’t bottom out but will follow the transition downward. If fishing it from the bank, you’re kind of limited to the top of the column (unless you like snagging constantly).

Kayak

11 minutes ago, LokiDawg said:

Kayak

I’d definitely try a 3-5’ crank from the bank out, and just back off the retrieve if you feel it getting into the salad. 

This sounds like a job for the Strike King Hybrid Hunter and Hybrid Hunter Shallow.  They have become my go to cranks for beating the riprap banks and around tule islands on the San Joaquin Delta. They come through vegetation better than any crank I have used.  Between the odd shaped bill that seams to work it through vegetation and it’s extreme buoyancy which lets you control depth by pausing or just raising your rod tip. the lure is great at negotiating vegetation.  You can even wake it over the dense subsurface stuff.  

You want an L bill crank.  L bills and weeds is the brother to a square bill and wood.  The L bill shapes deflects the bait over the weeds instead of wedging the weeds between the line and bill like a normal shallow crank/square bill.   

If the vegetation is a foot or two below the surface then I'll run a wakebait or a shallow running crankbait down as close the the vegetation as possible. 

If the vegetation is matted on the surface in large clumps then, if I can, I'll try to circle the mat and cast at it from different angles.

If the vegetation is widespread across the surface then I'll look for channels and try to run the crankbait through the channel.