Front shocks too loose? Better 60ft?

60' might be a tad slow, I was thinking it would be maybe 1.54 or so for the ET, but your 60'-1/8-1/4 and mph seems pretty consistent for what the car is going. If the car is consistently having the same 60', it's more than likely not spinning and hooking. Being you tried 2 different convertors and both ran the same, I'd say that more than likely your car is running what it's going to run for the combo you have.

I have a Uncle-in-law that has a Chevy that runs 9.70s. He tried 3 different convertors in his car. An 8" that was his original, another 8" was made specifically for his combo (He had his engine on dyno) and a buddies 9". Between all 3 convertors his car varied 1 tenth in the 1/4. One convertor would 60' better but than not mph as much as another. Now a good convertor will pick you up a ton over a stock or street style convertor, but unless your chasing every last .001 if you have a decent convertor doubt you will see much with a convertor change.

As far as shocks, I had the CE 3 way adjustable on my car for probably 10 years. Never had a issue with them til about last year. When running 1/4 mile the car would like wiggle when I got out of it, not all the time, but some of the time. I finally replaced them this past winter and the one shock was bad. It wouldn't adjust and was way easier to work than the other. The wiggle was from when I would lift the shock that was bad would allow that side of the front to come down quicker making the body sorta roll. I replaced them with QA1 Stocker shocks. Car still 60's the same. The car is smoother now when I lift and I have played with the adjustments to help tune my lights. My car is backhalved with a big tire and only running mid to high 10s.
I agree about the converter.. I don't think changing it will make a difference. If I ran at sea level my opinion might change. But for now I think the 1.56-1.58 is it's happy spot.