BBF,
Since you are in an automatic, starting in 3 isn't going to change anything up to 60mph. Manually selecting 1 or 2 in the shift gate only allows you to hold that gear regardless of RPM. But they are same gears the car uses if you were to just leave it in 3, just that it shift automatically.
60mph stock was about 7.5 seconds with the L48 190hp engine. If you've bumped it up about 100hp, you can likely expect to get into 6 seconds somewhere. To get your best manual shifts, it helps to know the powerband of your engine since the mods. Finding your peak torque is key for a 0-60 run. Use my engine as an example: I generate the most torque at 3250 rpms. So, in order to keep my car in that power band, I'll shift out of first gear around 3600 RPMs. That way when 2nd gear hits, I'm right back into my peak torque again.
As you're nearing the upper ranges of the 3K band, you should just about be clearing 60mph, give or take... so you see that 3rd gear isn't even used.
NOTE: When you have high RPMs at a slower speed, don't come off the throttle then shift into a higher gear. You'll SLAM that transmission which really beats up the entire driveline. Example: Dont turn 4500 RPMs in first, then let off the throttle and shift into 2nd gear as the RPMs are falling. BAD BAD BAD...
If I get into that situation, I'll either accelerate slightly again then upshift, or throw the car into neutral, wait a second, then drop it into 3rd. (Jst my experience...)