Keith,
I'm not sure the best way to 'snag' your aerator box. I had some crushed concrete pieces in my box to weigh it down. I wasn't sure I'd be able to snag it at all and was worried about snagging my aerator membrane with my metal-tined rake. The landscape rake has larger metal tines with flat tips rather than pointed tips like a bow rake. The landscape rake has closer spaced tines too. I just gently tried catching under the box and lifting it.

A weighted rope with a loop (lasso) on the end might allow you to hook under one of the diffusers and you could gently pull it up. The gravel doesn't weigh as much when under water so it will come up without too much force. It is best to let the water drain out before trying to hoist it in the boat as that WAS heavy.

I think I got lucky as some how the rake got under the small plastic lip on the side of the diffuser box. this is where the top half and the bottom half of the box comes together. There is nothing for it to grip but somehow the rake had continuous contact with one whole edge of the box and it continued to pull up as I slowly lifted it up.

Be sure you put a good stout rope, or cable and a float before dropping it back down. Even having a shoestring and a popbottle as a temporary fix helped me resnag it a couple of times with the rake much more easily before finally building the 4 part rope system.

My weighted rope is attached to the diffuser box with pvc cement and a hose clamp so if I had gripped the hose I was pulling gently enough that it would have probably been OK, but sharp objects vs the weighted tubing would not be so advisable. If you puncture weighted tubing right at the box you can always cut back a few inches and reattach. However if you pull on the weighted tubing from shore and the diffuser is embedded in the bottom like mine was you likely will just disconnect the tubing.. I think you would want to pull straight up and ideally not with the tubing only.