30Amp Sub Panel for EV Charger
1/2 inch conduit would accept 4 #10 thhn /thwn  conductors for your original  30 Amp design.

3/4 inch would  accept 4# 6 thhn / thwn for your 60 amp design, but not certain of your local code, where in some places, it will require 1".

What size panel is your MAIN  panel ? If it's 100 amps, I believe you are beyond the design limits. If your MAIN panel is 200 amps, you'll be fine with a 100 Amp Sub panel, as long as your MAIN it isn't loaded up with other stuff ...

The OTHER thing you're going to have to do when you wire that new sub panel...

REMOVE the tie ( jumper ) between the ground and neutral in the sub, if it has one..
...Unlike your MAIN has got, any sub panel must have that ground-to-neutral jumper removed.

This is for when you hook back up your existing 115v. circuits, if there is ever any faults to ground, they do not travel up the neutral that is in your sub panel.
 All ground faults will travel through the grounding conductor in your sub to your main.