I'm the last person you want to ask about racquets because I don't pay much attention. I once had several Wilson Pro Staffs and one was 383g while the lightest was 330g and I played with them all [OK, the 383g was noticeably heavier but I still played with it].
As you can tell by my username, I'm a net-crasher. I'm not necessarily more successful than someone who is more selective but I do put a lot of pressure on my opponent to pass me. As long as I can hit a decent approach and make them move or back up or get low, etc., I'm happy with my chances.
But you mentioned shank rate: that means you aren't making clean contact on your volleys, which could be due to taking your eye off of the ball, being too tense, not having fast enough reaction time, etc. Try actually watching the contact point when you volley: you can't actually see the ball hit the strings [it happens in 4ms] but you can force yourself to keep looking at that spot for a split second longer than what you're accustomed to. Maybe try it out in practice first. You might think you don't have enough time but you have more than you think.
Look at Gasquet volleying and how, especially on the BH, he's still looking to the side after he contacts the volley. This might help you.
I've always had very quick reaction time so that's never been a problem for me. I suggest you set up a practice session with someone consistent to feed you: start from the SL and tell him to hit medium-slow feeds. Concentrate on your form. Video yourself and review every minute or so to make sure you're dialed in.
If you're comfortable, have him increase the speed and still try to maintain good form and hit solid volleys [not spectacular winners]. Start trying to move the ball around a hit: go for sharper angles, straight down the middle right back at him, and the occasional drop volley. If your form ever breaks down consistently, have him slow down again. You can also start at the SL and move in with each subsequent volleys [I see 3 volleys then an OH; rinse and repeat].
Also, I play a fair amount of doubles and you are always having to hit reaction volleys where the opposing net man poaches and drills it at you and you just have to react as best as you can. I enjoy the challenge.